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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 5: Q. 101 (page 520)

Use the Definition of a Negative Exponent In the following exercises, simplify each expression.
$(a) {(\frac{5}{8})}^{- 2} (b) {(- \frac{b}{a})}^{- 2}$

Short Answer

Expert verified

The simplified expressions are:

$(a) {(\frac{5}{8})}^{- 2} = \frac{64}{25} (b) {(- \frac{b}{a})}^{- 2} = \frac{a^{2}}{b^{2}}$

Step by step solution

01

Step 1. Property for negative exponents

If $n$ is an integer and $a 鈮� 0$ , then

$a^{- n} = \frac{1}{a^{n}} o r \frac{1}{a^{- n}} = a^{n}$

02

Part a Step 1. Given expression

The given expression is ${(\frac{5}{8})}^{- 2}$

We have to simplify the given expression using negative exponents.

03

Part a Step 2. Simplify

Using a Property for negative exponents,

$\begin{matrix} {(\frac{5}{8})}^{鈭� 2} = {(\frac{8}{5})}^{2} \\ = \frac{64}{25} \end{matrix}$

So, the simplified expression is ${(\frac{5}{8})}^{- 2} = \frac{64}{25}$

04

Part b Step 1. Given information

The given expression is ${(- \frac{b}{a})}^{- 2}$

We have to simplify the given expression using negative exponents.

05

Part b Step 2. Simplify

Using a Property for negative exponents,

$\begin{matrix} {(鈭� \frac{b}{a})}^{鈭� 2} = {(鈭� \frac{a}{b})}^{2} \\ = \frac{a^{2}}{b^{2}} \end{matrix}$

So, the simplified expression is ${(- \frac{b}{a})}^{- 2} = \frac{a^{2}}{b^{2}}$

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Most popular questions from this chapter

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