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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 545 (page 1143)

Simplify
a) ${(- 49)}^{\frac{1}{2}}$
b) $- 49^{\frac{1}{2}}$
c) ${(49)}^{- \frac{1}{2}}$

Short Answer

Expert verified

Part (a) no real number

Part (b) $- 49^{\frac{1}{2}} =$ $- 7$

Part (c) ${(49)}^{- \frac{1}{2}} = \frac{1}{7}$

Step by step solution

01

Part (a) Step 1:Given infprmation

The given expression is ${(- 49)}^{\frac{1}{2}}$

02

Part (a) Step 2:Simplification

Rewrite as a square root. $\sqrt{- 49}$

There is no real number whose second power is $- 49$

03

Part (b) Step 1:Given information

The given expression is $- 49^{\frac{1}{2}}$

04

Part (b) Step 2:Simplification

The exponent only applies to the 49 $- {(49)}^{\frac{1}{2}}$

Rewrite as a square root. $- \sqrt{49}$

Simplify $7$

.

05

Part (c) Step 1:Given information

The given expression is ${(49)}^{- \frac{1}{2}}$

06

Part (c) Step 2:Simplification

Rewrite using the property $a^{- n} = \frac{1}{a^{n}}$ $\frac{1}{49^{\frac{1}{2}}}$

Rewrite as a square root. $\frac{1}{\sqrt{49}}$

Simplify $\frac{1}{7}$

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