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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 570 (page 1144)

Use the Laws of Exponents to Simplify Expressions with Rational Exponents
a) ${(m^{6})}^{\frac{5}{2}}$
b) ${(n^{9})}^{\frac{4}{3}}$
c) ${(p^{12})}^{\frac{3}{4}}$

Short Answer

Expert verified

Part (a) ${(m^{6})}^{\frac{5}{2}} = m^{15}$

Part (b) ${(n^{9})}^{\frac{4}{3}} = n^{12}$

Part (c) ${(p^{12})}^{\frac{3}{4}} = p^{9}$

Step by step solution

01

Part (a):Step 1:Given information

The given expression is ${(m^{6})}^{\frac{5}{2}}$

02

Part (a)Step 2:Simplification

To raise a power to a power, we multiply the exponents. $m^{6 . \frac{5}{2}}$

Simplify $m^{15}$

03

Part (b)Step 1:Given information

The given expression is ${(n^{9})}^{\frac{4}{3}}$

04

Part (b)Step 2:Simplification

To raise a power to a power, we multiply the exponents. $n^{9 . \frac{4}{3}}$

Simplify

05

Part (c)Step 1:Given information

The given expression is ${(p^{12})}^{\frac{3}{4}}$

06

Part (c)Step 2:Simplification

To raise a power to a power, we multiply the exponents. $p^{12 . \frac{3}{4}}$

Simplify $p^{9}$

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