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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 8: Q. 46 (page 756)

In the following exercises, simplify using absolute values as necessary.
$鈸� \sqrt[7]{128 r^{14}} 鈸� \sqrt[4]{81 s^{24}}$

Short Answer

Expert verified

Part(a) $\sqrt[7]{128 r^{14}} = 2 r^{2}$

Part(b) $\sqrt[4]{81 s^{24}} = 3 s^{6}$

Step by step solution

01

Part(a) Step 1. Given information

$鈸� \sqrt[7]{128 r^{14}}$

Simplify using absolute values as necessary.

02

Step 2. Explanation

$\begin{array}{l} Since \\ 鈬� 128 r^{14} = {(2 r^{2})}^{7} \\ 鈬� \sqrt[7]{128 r^{14}} \\ 鈬� \sqrt[7]{{(2 r^{2})}^{7}} \\ 鈬� 2 r^{2} \end{array}$

03

Part(b) Step 1. Given information

$鈸� \sqrt[4]{81 s^{24}}$

Simplify using absolute values as necessary.

04

Step 2. Explanation

$\begin{array}{l} Since \\ 鈬� 81 s^{24} = {(3 s^{6})}^{4} \\ 鈬� \sqrt[4]{81 s^{24}} \\ 鈬� \sqrt[4]{{(3 s^{6})}^{4}} \\ 鈬� 3 s^{6} \\ 鈬� \sqrt[4]{81 s^{24}} = 3 s^{6} \end{array}$

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Most popular questions from this chapter

Explain the difference of finding the $n^{t h}$ root of a number when the index is even compared to when the index is odd.

Use the Quotient Property to simplify square roots.

(a) $\sqrt{\frac{50 r^{5} s^{2}}{128 r^{2} s^{6}}}$

(b) $\sqrt[3]{\frac{24 m^{9} n^{7}}{375 m^{4} n}}$

(c) $\sqrt[4]{\frac{81 m^{2} n^{8}}{256 m n^{2}}}$

In the following exercises, simplify.

(a) $32^{\frac{2}{5}}$

(b) role="math" localid="1644741549807" $27^{- \frac{2}{3}}$

(c) ${(- 25)}^{\frac{1}{2}}$

In the following exercises, use the Product Property to simplify radical expressions $\sqrt{800}$

What is the difference between $9^{2}$ and $\sqrt{9}$ ?

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