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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 542 (page 1143)

Simplify
a) ${(- 1)}^{\frac{1}{3}}$
b) $- 1^{\frac{1}{3}}$
c) ${(1)}^{- \frac{1}{3}}$

Short Answer

Expert verified

Part (a) ${(- 1)}^{\frac{1}{3}} = - 1$

Part (b) $- 1^{\frac{1}{3}} = - 1$

Part (c) ${(1)}^{- \frac{1}{3}} = 1$

Step by step solution

01

Part (a) Step 1: Given information

The given expression is ${(- 1)}^{\frac{1}{3}}$

02

Part (b) Step 2:Simplification

Rewrite as a cube root. $\sqrt[3]{(- 1)}$

Rewrite -1 as ${(- 1)}^{3}$ $\sqrt[3]{{(- 1)}^{3}}$

Simplify $- 1$

03

Part (b) Step 1: Gievn information

The given expression is $- 1^{\frac{1}{3}}$

04

Part (b) Step 2:Simplification

The exponent applies only to the 1 $- {(1)}^{\frac{1}{3}}$

Rewrite as a cube root. $- \sqrt[3]{1}$

Rewrite 1 as $1^{3}$ $- \sqrt[3]{1^{3}}$

Simplify $- 1$

05

Part (c) Step 1:Given information

The given expression is ${(1)}^{- \frac{1}{3}}$

06

Part (c) Step 2:Simplification

Rewrite as a fraction with a positive exponent, using the property, $a^{- n} = \frac{1}{a^{n}}$

Write as a cube root. $\frac{1}{\sqrt[3]{1}}$

Rewrite 1 as $1^{3}$ $\frac{1}{\sqrt[3]{1^{3}}}$

Simplify $1$

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