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Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 9: Q 461 (page 1124)

Simplify a) $\sqrt[7]{128 r^{14}}$ b) $\sqrt[4]{81 s^{24}}$

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

The given expression is $\sqrt[7]{128 r^{14}}$ .

02

Part a) Step 2: Simplification

Using the formula of ${(a^{m})}^{\frac{1}{m}} = a^{m 脳 \frac{1}{m}}$

role="math" localid="1648838775349" $\sqrt[7]{128 r^{14}} = {(128 r^{14})}^{\frac{1}{7}} = {(2^{7} r^{14})}^{\frac{1}{7}} = 2^{7 脳 \frac{1}{7}} r^{14 脳 \frac{1}{7}} = 2 r^{2}$

Hence, $\sqrt[7]{128 r^{14}} = 2 r^{2}$

03

Part b) Step 1: Given information

The given expression is $\sqrt[4]{81 s^{24}}$ .

04

Part b) Step 2: Simplification

Using the formula of ${(a^{m})}^{\frac{1}{m}} = a^{m 脳 \frac{1}{m}}$

role="math" localid="1648839693617" $\sqrt[4]{81 s^{24}} = {(81 s^{24})}^{\frac{1}{4}} = {(3^{4} s^{24})}^{\frac{1}{4}} = 3^{4 脳 \frac{1}{4}} s^{24 脳 \frac{1}{4}} = 3 s^{6}$

Hence, $\sqrt[4]{81 s^{24}} = 3 s^{6}$

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Most popular questions from this chapter

Try It.

A helicopter dropped a rescue package from a height of $1, 296$ feet. Use the formula role="math" localid="1647883430342" $t = \frac{\sqrt{h}}{4}$ to find how many seconds it took for the package to reach the ground.

(a) Solve the equation $\sqrt{r + 4} - r + 2 = 0$

(b) Explain why one of the 鈥渟olutions鈥� that was found was not actually a solution to the equation.

In the following exercises, simplify and rationalize the denominator.

$\sqrt{\frac{3}{20}}$

In the following exercises, simplify and rationalize the denominator.

$- \frac{8}{3 \sqrt{6}}$

In the following exercises, solve:

$\sqrt{4 v + 3} = \sqrt{v - 6}$ .

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