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

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

Applying the Negative Exponent Property,

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

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

Short Answer

Step by step solution

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

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

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In the following exercises, simplify. Assume all variables are positive.(a) 216-14(b)-4932

Short Answer

Step by step solution

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

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

One App. One Place for Learning.

Most popular questions from this chapter

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