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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. 102 (page 520)

Use the Definition of a Negative Exponent In the following exercises, simplify each expression.
$(a) {(\frac{3}{10})}^{- 2} (b) {(- \frac{2}{z})}^{- 3}$

Short Answer

Expert verified

The simplified expressions are:

$(a) {(\frac{3}{10})}^{- 2} = \frac{100}{9} (b) {(- \frac{2}{z})}^{- 3} = - \frac{z^{3}}{8}$

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 information

The given expression is ${(\frac{3}{10})}^{- 2}$ .

We have to simplify the expression using negative exponents.

03

Part a Step 2. Simplify

Using the property for negative exponents,

$\begin{matrix} {(\frac{3}{10})}^{鈭� 2} = {(\frac{10}{3})}^{2} \\ = \frac{100}{9} \end{matrix}$

So, the simplified expression is ${(\frac{3}{10})}^{- 2} = \frac{100}{9}$

04

Part b Step 1. Given information

The given expression is ${(- \frac{2}{z})}^{- 3}$ .

We have to simplify the expression using negative exponents.

05

Part b Step 2. Simplify

Using the property for negative exponents,

$\begin{matrix} {(鈭� \frac{2}{z})}^{鈭� 3} = {(鈭� \frac{z}{2})}^{3} \\ = 鈭� \frac{z^{3}}{8} \end{matrix}$

So, the simplified expression is ${(- \frac{2}{z})}^{- 3} = - \frac{z^{3}}{8}$

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