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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 572 (page 1144)

Use the Laws of Exponents to Simplify Expressions with Rational Exponents
a) ${(x^{12})}^{\frac{2}{3}}$
b) ${(y^{20})}^{\frac{2}{5}}$
c) ${(z^{16})}^{\frac{1}{16}}$

Short Answer

Expert verified

Part (a) ${(x^{12})}^{\frac{2}{3}} = x^{8}$

Part (b) ${(y^{20})}^{\frac{2}{5}} = y^{8}$

Part (c) ${(z^{16})}^{\frac{1}{16}} = z$

Step by step solution

01

Part (a)Step 1:Given information

The given expression is ${(x^{12})}^{\frac{2}{3}}$

02

Part (a)Step 2:Simplification

To raise a power to a power, we multiply the exponents. $x^{12 . \frac{2}{3}}$

Simplify $x^{8}$

03

Part (b)Step 1:Given information

The given expression is ${(y^{20})}^{\frac{2}{5}}$

04

Part (b)Step 2:Simplification

To raise a power to a power, we multiply the exponents. $y^{20 . \frac{2}{5}}$

Simplify $y^{8}$

05

Part (c)Step 1:Given information

The given expression is ${(z^{16})}^{\frac{1}{16}}$

06

Part (c) Step 2:Simplification

To raise a power to a power, we multiply the exponents. $z^{16 . \frac{1}{16}}$

Simplify $z$

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Most popular questions from this chapter

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