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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 541 (page 1143)

Simplify
a) ${(- 243)}^{\frac{1}{5}}$
b) $- 243^{\frac{1}{5}}$
c) ${(243)}^{- \frac{1}{5}}$

Short Answer

Expert verified

Part (a) ${(- 243)}^{\frac{1}{5}} = - 3$

Part (b) $- 243^{\frac{1}{5}} = - 3$

Part (c) ${(243)}^{- \frac{1}{5}}$ $= \frac{1}{3}$

Step by step solution

01

Part (a) Step 1:Given information

The given expression is ${(- 243)}^{\frac{1}{5}}$

02

Part (a) Step 2:Simplification

Rewrite as a fifth root. $\sqrt[5]{(- 243)}$

Recognize 243 is a perfect fifth power. $\sqrt[5]{- {(3)}^{5}}$

Simplify. $- 3$

03

Part (b) Step 1:Given information

The given expression is $- 243^{\frac{1}{5}}$

04

Part (b) Step 2:Simplification

The exponent applies only to the 243. $- {(243)}^{\frac{1}{5}}$

Rewrite as a fifth root. $- \sqrt[5]{243}$

Rewrite 243 as $3^{5}$ $- \sqrt[5]{3^{5}}$

Simplify. $- 3$

05

Part (c) Step 1:Given information

The given expression is ${(243)}^{- \frac{1}{5}}$

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 fifth root. $\frac{1}{\sqrt[5]{243}}$

Rewrite 243 as $3^{5}$ $\frac{1}{\sqrt[5]{3^{5}}}$

Simplify, $\frac{1}{3}$

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