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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 730 (page 1152)

In the following exercises, simplify
$(a) \sqrt[3]{343 q^{7}} . (b) \sqrt[6]{192 r^{9}} .$

Short Answer

Expert verified

The simplification of the expressions are:

$(a) \sqrt[3]{343 q^{7}} = 7 q^{2} \sqrt[3]{q} . (b) \sqrt[6]{192 r^{9}} = 2 r \sqrt[6]{3 r^{3}} .$

Step by step solution

01

Part (a) Step 1. Given information

Given expression is $\sqrt[3]{343 q^{7}} .$

02

Part (a) Step 2. Simplification

$\sqrt[3]{343 q^{7}} = \sqrt[3]{7^{3} q^{6 + 1}} = \sqrt[3]{7^{3} q^{6} 脳 q^{1}} = \sqrt[3]{7^{3}} \sqrt[3]{q^{6}} \sqrt[3]{q} = {(7^{3})}^{\frac{1}{3}} 脳 {(q^{6})}^{\frac{1}{3}} 脳 {(q)}^{\frac{1}{3}} = 7 q^{2} \sqrt[3]{q} H e n c e, \sqrt[3]{343 q^{7}} = 7 q^{2} \sqrt[3]{q}$

03

Part (b) Step 1. Given information

Given expression is $\sqrt[6]{192 r^{9}} .$

04

Part (b) Step 2. Simplification

$\sqrt[6]{192 r^{9}} = \sqrt[6]{2^{6} 脳 3 r^{6 + 3}} = \sqrt[6]{2^{6} 脳 3 r^{6} 脳 r^{3}} = \sqrt[6]{2^{6}} \sqrt[6]{r^{6}} 脳 \sqrt[6]{3 r^{3}} = {(2^{6})}^{\frac{1}{6}} 脳 {(r^{6})}^{\frac{1}{6}} 脳 {(3 r^{3})}^{\frac{1}{6}} = 2 r \sqrt[6]{3 r^{3}} H e n c e, \sqrt[6]{192 r^{9}} = 2 r \sqrt[6]{3 r^{3}}$

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