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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 728 (page 1152)

In the following exercises, simplify
$(a) \sqrt[3]{54} . (b) \sqrt[4]{128} .$

Short Answer

Expert verified

The simplification of the expressions are:

$(a) \sqrt[3]{54} = 3 \sqrt[3]{2} . (b) \sqrt[4]{128} = 2 \sqrt[4]{8} .$

Step by step solution

01

Part (a) Step 1. Given information

The given expression is $\sqrt[3]{54} .$

02

Part (a) Step 2. Simplification

$\sqrt[3]{54} = \sqrt[3]{3^{3} 脳 2} = {(3^{3})}^{\frac{1}{3}} 脳 {(2)}^{\frac{1}{3}} = 3 \sqrt[3]{2} . H e n c e, \sqrt[3]{54} = 3 \sqrt[3]{2}$

03

Part (b) Step 1. Given information

The given expression is $\sqrt[4]{128} .$

04

Part (b) Step 2. Simplification

$\sqrt[4]{128} = \sqrt[4]{2^{7}} = \sqrt[4]{2^{4 + 3}} = \sqrt[4]{2^{4} 脳 2^{3}} = {(2^{4})}^{\frac{1}{4}} 脳 {(2^{3})}^{\frac{1}{4}} = 2 \sqrt[4]{8} H e n c e, \sqrt[4]{128} = 2 \sqrt[4]{8}$

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