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Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 9: Q 544 (page 1143)

Simplify
a) ${(- 81)}^{\frac{1}{4}}$
b) $- 81^{\frac{1}{4}}$
c) ${(81)}^{- \frac{1}{4}}$

Short Answer

Expert verified

Part (a) no real number

Part (b) $- 81^{\frac{1}{4}}$ $= - 3$

Part (c) ${(81)}^{- \frac{1}{4}} = \frac{1}{3}$

Step by step solution

01

Part (a) Step 1:Given information

The given expression is ${(- 81)}^{\frac{1}{4}}$

02

Part (b) Step 2:Simplification

Rewrite as a fourth root $\sqrt[4]{(- 81)}$

There is no real number whose fourth power is $- 81$ .

03

Part (b) Step 1:Given information

The given expression is $- 81^{\frac{1}{4}}$

04

Part (b) Step 2:Simplification

The exponent only applies to the 81 $- {(81)}^{\frac{1}{4}}$

Rewrite as a fourth root. $- \sqrt[4]{81}$

Rewrite 81 as $3^{4}$ $- \sqrt[4]{3^{4}}$

Simplify $- 3$

05

Part (c)Step 1:Given information

The given expression is ${(81)}^{- \frac{1}{4}}$

06

Part (c) Step 2:Simplification

Rewrite using the property $a^{- n} = \frac{1}{a^{n}}$ $\frac{1}{81^{\frac{1}{4}}}$

Rewrite as a fourth root. $\frac{1}{\sqrt[4]{81}}$

Rewrite 81 as $3^{4}$ $\frac{1}{\sqrt[4]{3^{4}}}$

Simplify, $\frac{1}{3}$

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Most popular questions from this chapter

In the following exercises, solve.

$\sqrt{d} - 2 = \sqrt{d - 20}$

In the following exercises, simplify by rationalizing the denominator

$\frac{\sqrt{5}}{\sqrt{n} - \sqrt{7}}$

Try It.

Katie wants to plant a square lawn in her front yard. She has enough sod to cover an area of $370$ square feet. Use the formula $s = \sqrt{A}$ to find the length of each side of her lawn. Round your answer to the nearest tenth of a foot.

In the following exercises, solve. Round approximations to one decimal place.

Landscaping Vince wants to

make a square patio in his yard.

He has enough concrete to pave

an area of 130 square feet. Use the

formula $s = \sqrt{A}$ to find the length

of each side of his patio. Round

your answer to the nearest tenth of a foot.

In the following exercises, simplify and rationalize the denominator.

$\frac{4}{\sqrt{5}}$

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