on numbers, brackets, or parentheses. At this rate, how many rotten mangoes will I have if l buy 100 mangoes?Ans: Suppose I have \(x\) rotten mangoes if I buy \(100\) mangoes. In the Import From Workspace dialog box, select . ln 2 = 0.6931. ", "acceptedAnswer": { "@type": "Answer", "text": "
Solving a proportion means that you are missing one part of one of the fractions, and you need to find that missing value.
Please enter 3 numbers and leave one field blank, then click Calculate button." If a/b = c/d, then b/a = d/c.
, The fourth term of a proportion is called the fourth proportional. This type describes the indirect relationship between two quantities. This formula can be used to find the percent of a given ratio and to find the missing value of a part of a whole. Learn more about us. A = 28, B = 34 and D =15 then C= 12.3529411765. On a mapof a sufficiently small geographical area, drawn to scaledistances, the distance between any two points on the map is directly proportional to the beeline distance between the two locations represented by those points; the constant of proportionality is the scale of the map. 2. The ratio is expressed employing a colon \(\left( : \right)\) or slash \(\left( / \right).\) The ratio is an expression. The properties of proportion that is followed by this relation . 1. It set up a relation between two or more quantities and thus helps in their comparison. Find out to know how your mom can be instrumental in your score improvement, (First In India): , , , , Remote Teaching Strategies on Optimizing Learners Experience, Area of Right Angled Triangle: Definition, Formula, Examples, Composite Numbers: Definition, List 1 to 100, Examples, Types & More, Electron Configuration: Aufbau, Pauli Exclusion Principle & Hunds Rule, Electrostatic Force: Coulombs Force & Applications. Exponent properties Calculator & Solver - SnapXam Exponent properties Calculator Get detailed solutions to your math problems with our Exponent properties step-by-step calculator. \dfrac {a} {b} = \dfrac {u} {v} ba = vu In the fraction form, a forward slash sign "/" is used between each pair of numbers. In simple words, if one quantity increases,the oppositequantity also increases and vice-versa. Polygon Calculator. Similarly, four quantities in continued proportion will have the ratio between the first and second equal to the ratio between the third and fourth. Here, \(2\) and \(64\) are extremes, and \(4\) and \(16\) are means. If you likeProportion Calculator, please consider adding a link to this tool by copy/paste the following code: Enter 3 numbers below and leave one field blank to solve for that value. For example, let us consider another example of the number of students in \(2\) classrooms where the ratio of the number of girls to boys is equal. Q.1: Are 36,49,6,7 in proportion?Ans: We have the product of extreme terms \( = 36 \times 7 = 252\)Product of means \( = 49 \times 6 = 294\)Therefore, the product of extreme terms \( \ne \) product of mean termsHence, \(36,49,6,7\) are not in proportion. We can apply the concepts of proportions to geography, comparing quantities in physics, dietetics, cooking, etc. If:=: after that: The proportion c,dc,dc,d and e,fe,fe,f would appear in the following way if the ratio layout is used. Your email address will not be published. A fraction, represented in the form of \(\mathbf{\frac{a}{b}}\), while ratio \(a:b\), then a proportion states that two ratios are equal. document.getElementById( "ak_js_1" ).setAttribute( "value", ( new Date() ).getTime() ); Statology is a site that makes learning statistics easy by explaining topics in simple and straightforward ways. The ratio is employed to match the dimensions of two things with an equivalent unit. 3. In biology, flowering plants are known by the name angiosperms. (2 + 3)/3 = (x + y)/y If 6:2=8:x, then 6x=16 If AX:XB as AB:AC, find the missing length.AX = 5, XB = 4, AC = 6, find AB. In the expression a/b = c/d, a and b are in the same proportion as c and d. A proportion is typically set up to solve a word problem in which one of its four quantities is unknown. If those ratios are, all the same, the table shows a proportional relationship. Let us proceed with the implication steps. How to use the summation calculator Input the expression of the sum Input the upper and lower limits Provide the details of the variable used in the expression Generate the results by clicking on the "Calculate" button. proportionality, In algebra, equality between two ratios. Embiums Your Kryptonite weapon against super exams! 4. One Proportion Z-Test Calculator A one proportion z-test is used to compare an observed proportion to a theoretical one. So just as a fraction of 3/30 can be simplified to 1/10, a ratio of 3:30 (or 4:40, 5:50, 6:60, and so on) can be simplified to 1:10. Ratio and Proportion Practice Questions: Properties of Proportion. The proportion of the population voting for Mr. Jones is. Since the denominators are also the same here, b d, you can remove them and say that: This is the result of cross multiplying the original equation: Proportion is explained majorly based on ratios and fractions. Order of Operations Factors & Primes Fractions Long Arithmetic Decimals Exponents & Radicals Ratios & Proportions Percent Modulo Mean, Median & Mode Scientific Notation Arithmetics. 5. A proportion is two ratios that have been set equal to each other, for example, 1/4 equals 2/8. 2. A ratio is a comparison of two quantities. Exponents may not be placed According to the above resultant statement, the value of A would be two times the value of B. 2D shape calculators 3D shape calculators Prime numbers Number . Derivative calculator Integral calculator Definite integrator Limit calculator Series calculator Equation solver Expression simplifier Factoring calculator Expression calculator Inverse function Taylor series Matrix calculator Matrix arithmetic Graphing calculator. In general, four numbers are in proportion if the ratio of the primary two quantities is equal to the last two. The Proportion Calculator is used to solve proportion problems and find the missing value in a proportion (Step by Step). This is shown as a proportion below. attempts to use the / symbol will result in an error. Middle School Math Solutions - Expand Calculator, Perfect Squares . Please enter 3 numbers and leave one field blank, then click Calculate button. For example, increasing the speed of the car will result in covering a fixed distance in less time. We will study the properties of proportion calculator or how to calculate proportion. We know that a fraction does not change when its numerator and denominator are multiplied or divided by the same non-zero number. FAQ What Is A Proportion? $$\mathbf{\frac{a}{b} = \frac{c}{d} \Rightarrow ad = bc}$$, $$\mathbf{\frac{a}{b} = \frac{c}{d} \Rightarrow \frac{b}{a} = \frac{d}{c}}$$, $$\mathbf{\frac{a}{b} = \frac{c}{d} \Rightarrow \frac{a}{c} = \frac{b}{d}}$$, $$\mathbf{\frac{a}{b} = \frac{c}{d} \Rightarrow \frac{a + b}{b} = \frac{c + d}{d}}$$, $$\mathbf{\frac{a}{b} = \frac{c}{d} \Rightarrow \frac{a b}{b} = \frac{c d}{d}}$$, $$\mathbf{\frac{a}{b + c} = \frac{b}{c + a} = \frac{c}{a + b}\ and\ a + b + c \neq0, then\ a = b = c}$$, $$\mathbf{\frac{a}{b} = \frac{c}{d} \Rightarrow \frac{a + b}{a b} = \frac{c + d}{c d}}$$, which is known as componendo -dividendo rule. Use the following as a guide: Variables Any lowercase letter may be used as a variable. en. A = 7, B = 13 and C = 6 then D = 11.1428571429, 3. How to Solve Proportion Problems with This Calculator? ln e = 1 since e = e. But, presumably, the most important natural logarithm is the one that calculates the value of a number between 1 and e, which turns out to be the number 2. So now you have: $$\mathbf{\frac{ad}{bd}=\frac{bc}{bd}}$$. Proportion finds application in solving manylifestyleproblemslikea business whilehandlingtransactions or cooking, etc. The Five Kingdom Classification system is a way of grouping living organisms. Check out our full list of online math calculators. Using the 68 95 99 Rule to Calculate Other Percentages. Basic proportions are of two types: direct proportions and inverse proportions. Componendo and dividendo If \(a : b = c : d\), then \(a + b : a b = c + d : c d\). Thus, if \(a,\,b,\,c\) are in continued proportion, then \(a,\,b,\,b,\,c\) are in proportion, i.e., \(a:b::b:c\), \(\Rightarrow \) product of extreme terms \(=\) product of mean terms, If \(a,\,b,\,c\) are in continued proportion, then \(b\) is the mean proportional between \(a\) and \(c.\), If \(b\) is the mean proportional between \(a\) and \(c,\) then \({b^2} = ac.\). Alternendo Property : If a/b = c/d, then a/c = b/d. If B has a value of 4, A would be 8.
, In proportion, the first and the last terms are called the extremes, whereas the second and the third terms are called the means. You can use this summation calculator to rapidly compute the sum of a series for certain expression over a predetermined range. A proportion is two ratios that have been set equal to each other, for example, 1/4 equals 2/8. A fraction with a zero denominator is undefined. Solution: Since the ratios in the proportion are reciprocated, we can use the second property of proportions. In the expression, $m$ equals $9$ and $n$ equals $2$, Simplify $\left(y^{12}\right)^2$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. It can be used to calculate the area of a regular polygon as well as various sided polygons such as 6 sided polygon, 11 sided polygon, or 20 sided shape, etc.It reduces the amount of time and efforts to find the area or any other property of a polygon. The reciprocal property of proportions. A ratio is a comparison of two quantities. 1 : to adjust (a part or thing) in size relative to other parts or things 2 : to make the parts of harmonious or symmetrical 3 : apportion, allot Phrases in proportion : proportional sense 1 Synonyms Noun balance coherence concinnity consonance consonancy harmony orchestration symmetry symphony unity See all Synonyms & Antonyms in Thesaurus Ratio Form Pandas: How to Use Variable in query() Function, Pandas: How to Create Bar Plot from Crosstab. A proportion between tworatios can be expressed using 2 forms. A Proportion Calculator is a free online tool that displays a proportion of a given expression. If a/b = c/d, then ad = bc. Calculate how much 7 pens cost. To understand the concept of ratio and proportion, go through the difference between ratio and proportion given here. This engineering data is often used in the design of structural beams . For example, the time taken by train to cover \(50km\ per\ hour\) is equal to the time taken by it to cover the distance of \(250\ km\ for\ 5\ hours\). Step 4: Use the cross-product rule. Keywords: definition; means extremes; Then hit "Calculate" and the test statistic and p-Value will be calculated for you. Be sure to enter something in each input box before clicking Suppose the value of 'x' is unknown. The first and fourth terms of the proportions are called extreme terms or extremes. = number of successes from group 1 = number of successes from group 2 = proportion of successes in group 1 = proportion of successes in group 2 State the null and alternative hypotheses and the level of significance Also, state your level here. Also, we have studied the properties of proportion, and different types of proportion and solved some example problems on the same. you can contact us anytime. Proportions are simple mathematical tools that use ratiosto definethe relation between multiple quantities. Proportion, in general, is referred to as a part, share, or number considered in comparative relation to a whole. Before we can use the calculator, it's important to understand what a proportion is and how to solve proportions by hand. Consider two ratios, \(3:24\) and \(4:36.\) We find that \(3:24 = 1:8\) and \(4:32 = 1:8.\) So, \(3:24 = 4:32\) is a proportion. In notation, an inverse proportion is written as \(y \propto \frac{1}{x}\). If the two resulting values are equal then the ratio is TRUE, otherwise is FALSE. In terms of present day algebra, letting the length of the shorter segment be one unit and the length of the longer segment be x units gives rise to the equation ( x + 1)/ x = x /1; this may be rearranged to form the quadratic equation x2 - x - 1 = 0, for which the positive solution is x = (1 + Square root of5 )/2, the golden ratio. Using it creatively, you can figure out other properties. Learn more about us. Find its fourth term.Ans: Let the fourth term be \(x.\)Then, \(3,5,21,\,x\) are in proportion.\( \Rightarrow 3 \times x = 5 \times 21\)\( \Rightarrow 3x = 5 \times 21\)\( \Rightarrow x = \frac{{5 \times 21}}{3}\)\( \Rightarrow x = 5 \times 7 = 35.\), Q.4: What must be added to the numbers 6,10,14 and 22 to be in proportion?Ans: Let the required number be \(x.\)Then, \(6 + x,\,10 + x,\,14 + x,\,22 + x\) are in proportion.\( \Rightarrow \) Product of extreme terms \(=\) product of mean terms.\( \Rightarrow \left( {6 + x} \right)\left( {22 + x} \right) = \left( {10 + x} \right)\left( {14 + x} \right)\)\( \Rightarrow 132 + 6x + 22x + {x^2} = 140 + 10x + 14x + {x^2}\)\( \Rightarrow 132 + 28x = 140 + 24x\)\( \Rightarrow 28x 24x = 140 132\)\( \Rightarrow 4x = 8\)\( \Rightarrow x = 2\)Hence, the required number is \(2.\), NCERT Solutions for Chapter-Ratio and Proportion. What are ratios and proportions? We can find the missing value by dividing the given values. Proportion is an equation. The power of a product is equal to the product of it's factors raised to the same power, Simplify $\left(x^2\right)^5$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. A Proportion Calculator is a free online tool that displays a proportion of a given expression. Practice your math skills and learn step by step with our math solver. Why Does the Cross Multiplication Calculator for Fractions Work? When we divide two amounts of the same sort, we get a ratio of the two quantities. Required fields are marked *. Great work. From mathematics, a proportion is simply two ratios in an equation, for example 1/2 = 50/100, 75/100 = 3/4, 9/10 = 90/100. (3 out of 5 is how many out of 40?) The formula to calculate this confidence interval is: To find a confidence interval for a population proportion, simply fill in the boxes below and then click the Calculate button. If either side of the proportion has a numerator and denominator that share a common factor with a variable, n: Thus, the continued proportion for the given ratios can be written in the form of \(ca:bc:bd\). Some useful properties of ratio and proportion are invertendo property, alternendo property, componendo Property, dividendo property, convertendo property, componendo-dividendo property, addendo property and equivalent ratio property. Copyright 2005 - 2023 Wyzant, Inc. - All Rights Reserved, Algebra Help Calculators, Lessons, and Worksheets, Fraction / Mixed Number Comparison Calculator, Associative Property of Addition and Multiplication, Consecutive Integer Word Problem Basics Worksheet, Combining Like Terms and Solving Worksheet, Factoring A Difference Between Two Squares Lessons, Factoring a Difference Between Two Squares Worksheet, Factoring A GCF From an Expression Lesson, Factoring a GCF From an Expression Worksheet, Determining the Equation of a Line From a Graph Worksheet, Determining the Equation of a Line Passing Through Two Points Worksheet, Determining x and y Intercepts From a Graph Worksheet, Simplifying Using The Order of Operations Worksheet, Simplifying Exponents of Polynomials Worksheet, Simplifying Exponents of Numbers Worksheet, Simplifying Exponents of Variables Lessons, Simplifying Exponents of Variables Worksheet, Simplifying Fractions With Negative Exponents Lesson, Negative Exponents in Fractions Worksheet, Simplifying Multiple Positive or Negative Signs Lessons, Simplifying Multiple Signs and Solving Worksheet, Simplifying Using the Distributive Property Lesson, Simplifying using the FOIL Method Lessons, Simplifying Variables With Negative Exponents Lessons, Variables With Negative Exponents Worksheet, Solve By Using the Quadratic Equation Lessons, Solving Using the Quadratic Formula Worksheet, Derivative of Lnx (Natural Log) Calculus Help, Using LHopitals Rule to Evaluate Limits, Converting Fractions, Decimals, and Percents, Multiplying Positive and Negative Numbers, Negative Fractions, Decimals, and Percents, Subtracting Positive and Negative Numbers, Angle Properties, Postulates, and Theorems, Proving Quadrilaterals Are Parallelograms, Inequalities and Relationship in a Triangle, Rules of Probability and Independent Events, Probability Distributions and Random Variables, Statistical Averages Mean, Mode, Median, Cumulative Frequency, Percentiles and Quartiles, Isolate X Effects of Cross Multiplication, Precalculus Help, Problems, and Solutions, Factorials, Permutations and Combinations, Consistent and Inconsistent Systems of Equations, Solving Systems of Equations by Matrix Method, Solving Systems of Equations by Substitution Method, Deriving Trig Identities with Eulers Formula, Algebra Applied Mathematics Word Problems, hocolate if the thermostat has a radius of 4 inches is 12 inches tall which formula could be used to find the number of cubic inches of hot chocolate needed to completely fill this thermos. Instructions: This calculator conducts a Chi-Square test for goodness of fit. Four numbers \(a,\,b,\,c,\,d\) are said to be in proportion if the ratio of the first two is equal to the ratio of the last two, i.e., \(a:b = c:d\). 2) The quantities a, b, c, and d are the "terms" of the proportion. To find . Of particular . You guys has made it so easy for me to calculate accurate proportion. Proportion is a mathematical comparison between two numbers. For addition and subtraction, use the standard + and symbols respectively. distributive-property-calculator. Cross Product Property : The product of the extremes equals the product of the means. The calculator uses cross multiplication to convert proportions into equations which Make sure one input should be unknown (x). This can also be written in form 1:4 = 4:16. Prefer to meet online? Step 4: Click on the "Reset" button to clear the fields and enter new values. If four numbers \(a,\,b,\,c,\,d\) are in proportion, we write \(a:b::c:d,\) which is read as \(a\) is to \(b\) as \(c\) is to \(d.\) Here, \(a\) is the first term, \(b\) is the second term, \(c\) is the third term, and \(d\) is the fourth term of the proportion. Enter 3 values and 1 unknown. For instance, consider that we have the following ratios. Embiums - Your Kryptonite weapon against super exams! For example, to express x2, enter x^2. This engineering calculator will determine the section modulus for the given cross-section. Cross multiplying works because youre just multiplying both sides of the equation by 1. Male gametes are created in the anthers of Amoeba is one of the fascinating organisms in nature. Consider that the value of X needs to be determined in the equation given below. The proportion between a,b and u,v would appear as follows if the fraction layout is used. In notation, the direct proportion is written as y x.
, If \(p:q = q:r,\) then \(p,\,q,\,r\) are said to be in continued proportion. \(c\) is called the third proportional to \(a\) and \(b\). BYJUS online proportion calculator tool makes the calculation faster, and it displays the true or false in a fraction of seconds. Leading AI Powered Learning Solution Provider, Fixing Students Behaviour With Data Analytics, Leveraging Intelligence To Deliver Results, Exciting AI Platform, Personalizing Education, Disruptor Award For Maximum Business Impact, Copyright 2023, Embibe. Three quantities a, b, c of the same kind (in same units) are said to be in continuous proportion. 3. Find the missing fraction variable in the proportion using cross multiplication to calculate the unknown variable \(x\). \(\mathbf{x = \frac{(4 \times 15)}{10}}\), To check the work put the result, 6 back into the original equation. A proportion is an equation or equality of the two ratios, and we can write proportions to estimate equivalent ratios and work for unknown quantities. To solve fractions for unknown x using this proportion solver, follow the below steps: After pressing the button, you will get the value of unknown x and a step-by-step solution by cross multiplication and proportion method. Solve for an unknown value \(x\) with this fractions calculator. We all know that a proportion is an expression which states that the two ratios are equal. Is light a wave or a particle? Once you click away on our proportional relationship calculator and determine two variables that are directly or indirectly proportional to each other in a fraction of seconds. Thus, multiplying the first ratio by c and the second ratio by b, we have. } }]} Your email address will not be published. Solution: Let the fourth proportional be x. Step 2: Create a mathematical equation that describes the situation. . Continue reading this article to learn everything there is to know about Ratios and Proportions, including basic vocabulary, properties, formulas, and examples. Statology Study is the ultimate online statistics study guide that helps you study and practice all of the core concepts taught in any elementary statistics course and makes your life so much easier as a student. Each tool is carefully developed and rigorously tested, and our content is well-sourced, but despite our best effort it is possible they contain errors. In the above sets of ratios, c will be multiplied by q and d will be multiplied by p. 2 * 2 = 1 * 4 4 = 4 $\frac{\left(\left(3x y^2\right)^4\left(2x^3 y^4\right)^3\right)^2}{\left(4x^2 y^3\right)^5}$, $\frac{\left(\left(3xy^2\right)^4\left(2x^3y^4\right)^3\right)^2}{4^5\left(x^2y^3\right)^5}$, $\frac{\left(\left(3xy^2\right)^4\left(2x^3y^4\right)^3\right)^2}{4^5\left(x^2\right)^5\left(y^3\right)^5}$, $\frac{\left(\left(3xy^2\right)^4\right)^2\left(\left(2x^3y^4\right)^3\right)^2}{4^5\left(x^2\right)^5\left(y^3\right)^5}$, $\frac{\left(3^4\left(xy^2\right)^4\right)^2\left(\left(2x^3y^4\right)^3\right)^2}{4^5\left(x^2\right)^5\left(y^3\right)^5}$, $\frac{\left(3^4\right)^2\left(\left(xy^2\right)^4\right)^2\left(\left(2x^3y^4\right)^3\right)^2}{4^5\left(x^2\right)^5\left(y^3\right)^5}$, $\frac{\left(3^4\right)^2\left(x^4\left(y^2\right)^4\right)^2\left(\left(2x^3y^4\right)^3\right)^2}{4^5\left(x^2\right)^5\left(y^3\right)^5}$, $\frac{\left(3^4\right)^2\left(x^4\right)^2\left(\left(y^2\right)^4\right)^2\left(\left(2x^3y^4\right)^3\right)^2}{4^5\left(x^2\right)^5\left(y^3\right)^5}$, $\frac{\left(3^4\right)^2\left(x^4\right)^2\left(\left(y^2\right)^4\right)^2\left(2^3\left(x^3y^4\right)^3\right)^2}{4^5\left(x^2\right)^5\left(y^3\right)^5}$, $\frac{\left(3^4\right)^2\left(x^4\right)^2\left(\left(y^2\right)^4\right)^2\left(2^3\right)^2\left(\left(x^3y^4\right)^3\right)^2}{4^5\left(x^2\right)^5\left(y^3\right)^5}$, $\frac{\left(3^4\right)^2\left(x^4\right)^2\left(\left(y^2\right)^4\right)^2\left(2^3\right)^2\left(\left(x^3\right)^3\left(y^4\right)^3\right)^2}{4^5\left(x^2\right)^5\left(y^3\right)^5}$, $\frac{\left(3^4\right)^2\left(x^4\right)^2\left(\left(y^2\right)^4\right)^2\left(2^3\right)^2\left(\left(x^3\right)^3\left(y^4\right)^3\right)^2}{1024\left(x^2\right)^5\left(y^3\right)^5}$, $\frac{81^2\left(x^4\right)^2\left(\left(y^2\right)^4\right)^2\left(2^3\right)^2\left(\left(x^3\right)^3\left(y^4\right)^3\right)^2}{1024\left(x^2\right)^5\left(y^3\right)^5}$, $\frac{6561\left(x^4\right)^2\left(\left(y^2\right)^4\right)^2\left(2^3\right)^2\left(\left(x^3\right)^3\left(y^4\right)^3\right)^2}{1024\left(x^2\right)^5\left(y^3\right)^5}$, $\frac{6561\left(x^4\right)^2\left(\left(y^2\right)^4\right)^28^2\left(\left(x^3\right)^3\left(y^4\right)^3\right)^2}{1024\left(x^2\right)^5\left(y^3\right)^5}$, $\frac{6561\cdot 64\left(x^4\right)^2\left(\left(y^2\right)^4\right)^2\left(\left(x^3\right)^3\left(y^4\right)^3\right)^2}{1024\left(x^2\right)^5\left(y^3\right)^5}$, $\frac{419904\left(x^4\right)^2\left(\left(y^2\right)^4\right)^2\left(\left(x^3\right)^3\left(y^4\right)^3\right)^2}{1024\left(x^2\right)^5\left(y^3\right)^5}$, $\frac{419904\left(x^4\right)^2\left(\left(y^2\right)^4\right)^2\left(\left(x^3\right)^3\left(y^4\right)^3\right)^2}{1024x^{2\cdot 5}\left(y^3\right)^5}$, $\frac{419904\left(x^4\right)^2\left(\left(y^2\right)^4\right)^2\left(\left(x^3\right)^3\left(y^4\right)^3\right)^2}{1024x^{2\cdot 5}y^{3\cdot 5}}$, $\frac{419904x^{4\cdot 2}\left(\left(y^2\right)^4\right)^2\left(\left(x^3\right)^3\left(y^4\right)^3\right)^2}{1024x^{2\cdot 5}y^{3\cdot 5}}$, $\frac{419904x^{4\cdot 2}\left(y^2\right)^{4\cdot 2}\left(\left(x^3\right)^3\left(y^4\right)^3\right)^2}{1024x^{2\cdot 5}y^{3\cdot 5}}$, $\frac{419904x^{4\cdot 2}y^{2\cdot 4\cdot 2}\left(\left(x^3\right)^3\left(y^4\right)^3\right)^2}{1024x^{2\cdot 5}y^{3\cdot 5}}$, $\frac{419904x^{4\cdot 2}y^{2\cdot 4\cdot 2}\left(x^{3\cdot 3}\left(y^4\right)^3\right)^2}{1024x^{2\cdot 5}y^{3\cdot 5}}$, $\frac{419904x^{4\cdot 2}y^{2\cdot 4\cdot 2}\left(x^{3\cdot 3}y^{4\cdot 3}\right)^2}{1024x^{2\cdot 5}y^{3\cdot 5}}$, $\frac{419904x^{4\cdot 2}y^{2\cdot 4\cdot 2}\left(x^{3\cdot 3}y^{4\cdot 3}\right)^2}{1024x^{10}y^{3\cdot 5}}$, $\frac{419904x^{4\cdot 2}y^{2\cdot 4\cdot 2}\left(x^{3\cdot 3}y^{4\cdot 3}\right)^2}{1024x^{10}y^{15}}$, $\frac{419904x^{8}y^{2\cdot 4\cdot 2}\left(x^{3\cdot 3}y^{4\cdot 3}\right)^2}{1024x^{10}y^{15}}$, $\frac{419904x^{8}y^{8\cdot 2}\left(x^{3\cdot 3}y^{4\cdot 3}\right)^2}{1024x^{10}y^{15}}$, $\frac{419904x^{8}y^{16}\left(x^{3\cdot 3}y^{4\cdot 3}\right)^2}{1024x^{10}y^{15}}$, $\frac{419904x^{8}y^{16}\left(x^{9}y^{4\cdot 3}\right)^2}{1024x^{10}y^{15}}$, $\frac{419904x^{8}y^{16}\left(x^{9}y^{12}\right)^2}{1024x^{10}y^{15}}$, $\frac{419904x^{8}y^{\left(16-15\right)}\left(x^{9}y^{12}\right)^2}{1024x^{10}}$, $\frac{419904x^{8}y^{1}\left(x^{9}y^{12}\right)^2}{1024x^{10}}$, $\frac{419904x^{8}y\left(x^{9}y^{12}\right)^2}{1024x^{10}}$, $\frac{419904y\left(x^{9}y^{12}\right)^2}{1024x^{\left(10-8\right)}}$, $\frac{419904y\left(x^{9}y^{12}\right)^2}{1024x^{2}}$, $\frac{419904y\left(x^{9}\right)^2\left(y^{12}\right)^2}{1024x^{2}}$, $\frac{419904yx^{9\cdot 2}\left(y^{12}\right)^2}{1024x^{2}}$, $\frac{419904yx^{9\cdot 2}y^{12\cdot 2}}{1024x^{2}}$, $\frac{419904yx^{18}y^{12\cdot 2}}{1024x^{2}}$, $\frac{419904y^{\left(24+1\right)}x^{18}}{1024x^{2}}$, $\frac{419904y^{25}x^{\left(18-2\right)}}{1024}$, $\frac{\sqrt{2x^{12} y^{21} z^8}}{40\sqrt{xy\cdot z}}$, $\left(x\left(x^{2\left(x\left(x^2\right)^{\frac{1}{3}}\right)^{\frac{1}{3}}}\right)^{\frac{1}{3}}\right)^{\frac{1}{3}}$, $\left(7x^{\frac{2}{3}}\left(x y^{121\left(-1\right)}\right)^{\frac{1}{2}}\right)^4$, $\left(1\left(81\right)\left(-1\right)\right)^{\frac{1}{4}}$, $\frac{\left(x^{\frac{1}{5}} y^{\frac{3}{2}}\right)^{10}}{\left(y^{\left(-1\right)\cdot\frac{2}{5}} x^{\frac{2}{3}}\right)^5}$, $\frac{\left(4x^{121\left(-1\right)} y^4 z^8\right)^3}{\left(9x y^3 z^5\right)^4}$, $\frac{\left(-5x^3 y^2\right)^3\left(x y^5\right)^2}{\left(-5x^{-1}\cdot y\right)^{-1}}$.