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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. 108 (page 520)

Use the definition of Negative Exponent to simplify (a) $3 路 4^{- 2}$ (b) ${(3 路 4)}^{- 2}$

Short Answer

Expert verified

The simplified equation is (a) $\frac{3}{16}$ (b) $\frac{1}{144} .$

Step by step solution

01

Part (a). Step 1. Given information.

The given expression is $3 路 4^{- 2}$ .

We have to simplify the equation.

02

Part (a). Step 2. Definition of Negative exponents.

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 exponents

$3 路 4^{- 2} = 3 路 {(\frac{1}{4})}^{2} = 3 路 (\frac{1}{16}) = \frac{3}{16} .$

So, $3 路 4^{- 2} = \frac{3}{16} .$

04

Part (b). Step 1. Given information.

The given expression is ${(3 路 4)}^{- 2} .$

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 exponents

${(3 路 4)}^{- 2} = {(\frac{1}{3} 路 \frac{1}{4})}^{2} = \frac{1}{12^{2}} = \frac{1}{144}$ .

So, ${(3 路 4)}^{- 2} = \frac{1}{144} .$

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