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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. 104 (page 520)

Use the definition of a Negative Exponent to simplify $(a) {(\frac{7}{2})}^{- 3} (b) {(- \frac{3}{x})}^{- 3}$ .

Short Answer

Expert verified

The simplified equation is $(a) \frac{8}{343} (b) - \frac{x^{3}}{27} .$

Step by step solution

01

Part a Step 1. Given information

The given expression is ${(\frac{7}{2})}^{- 3}$ .

We have to simplify the expression.

02

Part a Step 2. Definition of Negative Exponent.

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

$a^{- n} = \frac{1}{a^{n}}$ .

03

Part a. Step 3. Simplify the expression.

Using the definition of Negative exponent

${(\frac{7}{2})}^{- 3} = {(\frac{2}{7})}^{3} = \frac{8}{343}$

So, ${(\frac{7}{2})}^{- 3} = \frac{8}{343} .$

04

Part b. Step 1. Given information.

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

We have to simplify the expression.

05

Part (b). Step 2. Definition of Negative Exponents.

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

$a^{- n} = \frac{1}{a^{n}} .$

06

Part (b). Step 3. Simplify the expression.

Using the definition of Negative exponent

${(- \frac{3}{x})}^{- 3} = {(- \frac{x}{3})}^{3} = - \frac{x^{3}}{27} .$

So, ${(- \frac{3}{x})}^{- 3} = - \frac{x^{3}}{27} .$

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