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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 9.178. (page 1113)

Simplify a) $\sqrt[3]{- 216}$ b) $\sqrt[4]{- 81}$ c) $\sqrt[5]{- 1024}$

Short Answer

Expert verified

Part (a) $\sqrt[3]{- 216} = - 6$

Part (b) role="math" localid="1649335395335" $\sqrt[4]{- 81} =$ Not a real number.

Part (c) $\sqrt[5]{- 1024} = - 4$

Step by step solution

01

Part (a) Step 1 : Given Information

The given expression is $\sqrt[3]{- 216}$ .

02

Part (a) Step 2: Simplification

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

localid="1648703874458" $\sqrt[3]{- 216} = {(- 216)}^{\frac{1}{3}} = ({(- 6)}^{3})^{\frac{1}{3}} = {(- 6)}^{3 脳 \frac{1}{3}} = - 6$

Hence, $\sqrt[3]{- 216} = - 6$ .

03

Part (b) Step 1: Given information

The given expression is $\sqrt[4]{- 81}$ .

04

Part (b) Step 2: Simplification

Simplify $\sqrt[4]{- 81}$ as shown.

No real number raised to the fourth power is positive.

So, it is,

Not a real number.

05

Part (c) Step 1: Given information

The given expression is $\sqrt[5]{- 1024}$ .

06

Part (c) Step 2: Simplification

Simplify $\sqrt[5]{- 1024}$ as shown.

localid="1649336555621" $\sqrt[5]{- 1024} = {(- 1024)}^{\frac{1}{5}} = {(- 4^{5})}^{\frac{1}{5}} = - 4$

Hence, localid="1649336659163" $\sqrt[5]{- 1024} = - 4$ .

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Most popular questions from this chapter

In the following exercises, simplify and rationalize the denominator.

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