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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 8: Q. 583. (page 857)

In the following exercises, simplify. Assume all variables are positive.
(a) $216^{- \frac{1}{4}}$
(b) $- 49^{\frac{3}{2}}$

Short Answer

Expert verified

The simplified forms are,

(a) ${(\frac{1}{216})}^{\frac{1}{4}}$

(b) $343 i$

Step by step solution

01

Part (a) Step 1. Simplify the given number.

Applying the Negative Exponent Property,

$216^{- \frac{1}{4}} = \frac{1}{216^{\frac{1}{4}}} = {(\frac{1}{216})}^{\frac{1}{4}}$

02

Part (b) Step 1. Simplify the given number.

Applying the Power Property

- 49^{\frac{3}{2}} = {(- 49^{3})}^{\frac{1}{2}} = {(- 117649)}^{^{\frac{1}{2}}} = \sqrt{- 117649} = \sqrt{- 1} \sqrt{- 117649} = 343 i

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