/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 38 Simplify by factoring. $$ \s... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 10: Problem 38

Simplify by factoring. $$ \sqrt[3]{27 a b^{6}} $$

Short Answer

Expert verified
The simplified form is \(3 a^{1/3} b^2\).

Step by step solution

01

- Write the expression in exponential form

Rewrite the cube root as a fractional exponent. \[\sqrt[3]{27 a b^{6}} = (27 a b^{6})^{1/3} \]
02

- Factor inside the radical

Factor the expression inside the parentheses. \[ 27 a b^{6} = 3^3 \times a \times (b^2)^3 \]
03

- Apply the exponent

Distribute the exponent \(\frac{1}{3}\) to each factor inside the parentheses. \[ (3^3 \times a \times (b^2)^3)^{1/3} = 3^{3/3} \times a^{1/3} \times (b^2)^{3/3} \]
04

- Simplify the exponents

Simplify the exponents. \[ 3 \times a^{1/3} \times b^2 \]

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Factorization
Factorization is the process of breaking down an expression into simpler elements, or

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Review simplifying rational expressions (Sections\(7.1-7.5)\) Perform the indicated operation and, if possible, simplify. $$ \frac{15 a^{2} x}{8 b} \cdot \frac{24 b^{2} x}{5 a}[7.2] $$

Review simplifying rational expressions (Sections\(7.1-7.5)\) Perform the indicated operation and, if possible, simplify. $$ \frac{\frac{1}{x+1}-\frac{2}{x}}{\frac{3}{x}+\frac{1}{x+1}}[7.5] $$

Simplify. $$ (1-i)^{3}(1+i)^{3} $$

Find the midpoint of each segment with the given endpoints. \((-3.4,8.1)\) and \((4.8,-8.1)\)

Perform the indicated operation and simplify. Assume that all variables represent positive real numbers. $$\sqrt[4]{a^{2} b}(\sqrt[3]{a^{2} b}-\sqrt[5]{a^{2} b^{2}})$$
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Probability and Statistics

Read Explanation

Statistics

Read Explanation

Pure Maths

Read Explanation

Decision Maths

Read Explanation

Discrete Mathematics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.