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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 565. (page 1144)

Simplify : $a) - 49^{\frac{3}{2}} b) - 49^{\frac{- 3}{2}} c) {(- 49)}^{\frac{3}{2}} .$

Short Answer

Expert verified

Part a) $- 49^{\frac{3}{2}} = - 343 .$

Part b) $- 49^{(- \frac{3}{2})} = - \frac{1}{343}$

Part c)localid="1651817470061" ${(- 49)}^{\frac{3}{2}}$ is not a real number.

Step by step solution

01

Part (a) Step 1 : Given Information

The given expression is $- 49^{\frac{3}{2}} .$

02

Part (a) Step 2: Simplification

$- 49^{\frac{3}{2}} = {(- 7)}^{2 脳 \frac{3}{2}} = {(- 7)}^{3} = - 343 H e n c e, - 49^{\frac{3}{2}} = - 343 .$

03

Part (b) Step 1: Given information

The given expression is $- 49^{\frac{- 3}{2}}$ .

04

Part (b) Step 2: Simplification

$- 49^{\frac{- 3}{2}} = {(- 7)}^{2 脳 \frac{- 3}{2}} = {(- 7)}^{- 3} = - \frac{1}{343} H e n c e, - 49^{\frac{- 3}{2}} = - \frac{1}{343} .$

05

Part (c) Step 1: Given information

The given expression is ${(- 49)}^{\frac{3}{2}} .$

06

Part (c) Step 2: Simplification

The square root of a negative number is not a real number.

Hence, ${(- 49)}^{\frac{3}{2}}$ is not a real number.

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