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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. 103 (page 520)

Use the Definition of a Negative Exponent In the following exercises, simplify each expression.
$(a) {(\frac{4}{9})}^{- 3} (b) {(- \frac{u}{v})}^{- 5}$

Short Answer

Expert verified

The simplified expressions are:

$(a) {(\frac{4}{9})}^{- 3} = \frac{729}{64} (b) {(- \frac{u}{v})}^{- 5} = - \frac{v^{5}}{u^{5}}$

Step by step solution

01

Step 1. Property for negative exponent

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 information

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

We have to simplify the expression using property for negative exponents.

03

Part a Step 2. Simplify

Using property for negative exponents,

$\begin{matrix} {(\frac{4}{9})}^{鈭� 3} = {(\frac{9}{4})}^{3} \\ = \frac{729}{64} \end{matrix}$

So, the simplified expression is ${(\frac{4}{9})}^{- 3} = \frac{729}{64}$

04

Part b Step 1. Given information

The given expression is ${(- \frac{u}{v})}^{- 5}$ .

We have to simplify the expression using property for negative exponents.

05

Part b Step 2.Simplify

Using property for negative exponents,

$\begin{matrix} {(鈭� \frac{u}{v})}^{鈭� 5} = {(鈭� \frac{v}{u})}^{5} \\ = 鈭� \frac{v^{5}}{u^{5}} \end{matrix}$

So, the simplified expression is ${(- \frac{u}{v})}^{- 5} = - \frac{v^{5}}{u^{5}}$

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Most popular questions from this chapter

In the following exercises , simplify the expression $(\frac{1}{5} f^{8}) (20 鈥� f^{3}) 鈥�$ .

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