Homework Help is Here – Start Your Trial Now!
Math
Algebra
216xº yª + )2 (81x1ºy®

216xº yª + )2 (81x1ºy®

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
See similar textbooks
icon
Related questions
Question

Simplify the expression show all steps assume variables are positive 

### Expression Simplification The mathematical expression given is: \[ \sqrt[3]{216x^9 y^4} + (81x^{10} y^8)^{\frac{1}{2}} \] #### Explanation: 1. **Cubic Root Expression:** - The first term is the cube root of \(216x^9 y^4\). This involves finding a value that when multiplied by itself three times will yield \(216x^9 y^4\). 2. **Square Root Expression:** - The second term is \((81x^{10} y^8)^{\frac{1}{2}}\), which is the square root of \(81x^{10} y^8\). This involves finding a value that when multiplied by itself will yield \(81x^{10} y^8\). #### Steps to Simplification: - For the cubic root: - Break down \(216\) into its prime factors or recognize it as a cube of a simpler number. - Simplify the expression for \(x^9\) and \(y^4\) by dividing each exponent by three. - For the square root: - Simplify \(81\) by recognizing it as a power of a smaller number. - Simplify the expression for \(x^{10}\) and \(y^8\) by dividing each exponent by two. This typically involves recognizing perfect cubes and squares and applying exponent rules to simplify each term.
Transcribed Image Text:### Expression Simplification The mathematical expression given is: \[ \sqrt[3]{216x^9 y^4} + (81x^{10} y^8)^{\frac{1}{2}} \] #### Explanation: 1. **Cubic Root Expression:** - The first term is the cube root of \(216x^9 y^4\). This involves finding a value that when multiplied by itself three times will yield \(216x^9 y^4\). 2. **Square Root Expression:** - The second term is \((81x^{10} y^8)^{\frac{1}{2}}\), which is the square root of \(81x^{10} y^8\). This involves finding a value that when multiplied by itself will yield \(81x^{10} y^8\). #### Steps to Simplification: - For the cubic root: - Break down \(216\) into its prime factors or recognize it as a cube of a simpler number. - Simplify the expression for \(x^9\) and \(y^4\) by dividing each exponent by three. - For the square root: - Simplify \(81\) by recognizing it as a power of a smaller number. - Simplify the expression for \(x^{10}\) and \(y^8\) by dividing each exponent by two. This typically involves recognizing perfect cubes and squares and applying exponent rules to simplify each term.
Expert Solution
Step 1

Given.

We are given an equation in X and Y such that

f(x) = ³√(216x⁹y⁴) +√(81x10y⁸)

Now we know that

³√x = x1/3 and √x = x1/2

steps

Step by step

Solved in 2 steps with 1 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education
SEE MORE TEXTBOOKS