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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 9.232 (page 1141)

Simplify:
a) ${(16 m^{\frac{1}{3}})}^{\frac{3}{2}}$
b) ${(81 n^{\frac{2}{5}})}^{\frac{3}{2}}$

Short Answer

Expert verified

a) ${(16 m^{\frac{1}{3}})}^{\frac{3}{2}} = 64 m^{\frac{1}{2}}$

b) $729 n^{\frac{3}{5}}$

Step by step solution

01

Part (a) Step 1: Given Information

The given expression is ${(16 m^{\frac{1}{3}})}^{\frac{3}{2}}$ .

02

Part (a) Step 2: Simplification

${(16 m^{\frac{1}{3}})}^{\frac{3}{2}}$

Use product to a power property

$= 16^{\frac{3}{2}} {(m^{\frac{1}{3}})}^{\frac{3}{2}}$

Write $16$ as a power of $2$

$= {(4^{2})}^{\frac{3}{2}} {(m^{\frac{1}{3}})}^{\frac{3}{2}}$

To raise power to a power, we multiply exponents

$= 4^{3} m^{\frac{1}{2}}$

$= 64 m^{\frac{1}{2}}$

03

Part (b) Step 1: Given Information

The given expression is ${(81 n^{\frac{2}{5}})}^{\frac{3}{2}}$ .

04

Part (b) Step 2: Simplification

${(81 n^{\frac{2}{5}})}^{\frac{3}{2}}$

Use product to power property

$= 81^{\frac{3}{2}} {(n^{\frac{2}{5}})}^{\frac{3}{2}}$

Write $81$ as power of $2$

$= {(9^{2})}^{\frac{3}{2}} {(n^{\frac{2}{5}})}^{\frac{3}{2}}$

$= 729 n^{\frac{3}{5}}$

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