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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. 132. (page 522)

In the following exercises, simplify each expression.
$(a) . 6 r^{- 1} (b) . {(6 r)}^{- 1} (c) . {(- 6 r)}^{- 1}$

Short Answer

Expert verified

The simplified form of the expressions

$(a) . 6 r^{- 1} = \frac{6}{r} (b) . {(6 r)}^{- 1} = \frac{1}{6 r} (c) . {(- 6 r)}^{- 1} = - \frac{1}{6 r}$

Step by step solution

01

Part (a) Step 1. Given information.

The given expression is $6 r^{- 1} .$

02

Part (a) Step 2. Calculate the expression.

Apply the concept of negative exponents.

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

So,

$6 r^{- 1} = \frac{6}{r}$

03

Part (b) Step 1. Given information.

The given expression is ${(6 r)}^{- 1}$ .

04

Part (b) Step 2. Calculate the expression.

Apply the concept of negative exponent.

${(a b)}^{- n} = \frac{1}{{(a b)}^{n}}$

So,

${(6 r)}^{- 1} = \frac{1}{6 r}$ .

05

Part (c) Step 1. Given information.

The given expression is ${(- 6 r)}^{- 1}$ .

06

Part (c) Step 2. Calculate the expression.

Apply the concept of negative exponent.

${(- a b)}^{- 1} = \frac{1}{- a b}$ .

So,

${(- 6 r)}^{- 1} = \frac{1}{- 6 r} .$

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