Chapter 8: Q. 8.64 (page 781)

Simplify:
(a) $- 81^{\frac{3}{2}}$ -
(b) $- 81^{- \frac{3}{2}}$
(c) ${(- 81)}^{- \frac{3}{2}}$

Short Answer

Expert verified

The simplification of $- 81^{\frac{3}{2}}$ is $- 729$

The simplification of $- 81^{- \frac{3}{2}}$ is $- \frac{1}{729}$

The simplification of ${(- 81)}^{- \frac{3}{2}}$ has no real root.

Step by step solution

Part (a) Step 1. Given

An expression $- 81^{\frac{3}{2}}$

To simplify the given expression

Part (a) Step 2. Rewrite in radical form and simplify

Rewrite in radical form and simplify.

$- 81^{\frac{3}{2}} = - {(\sqrt{81})}^{3}$

$= - {(\sqrt{9^{2}})}^{3}$

$= - 9^{3}$

$= - 729$

Part (b) Step 1. Given

An expression $- 81^{- \frac{3}{2}}$

To simplify the given expression

Part (b) Step 2. Rewrite in radical form and simplify

By the property, $a^{- n} = \frac{1}{a^{n}}$ ,

$- 81^{- \frac{3}{2}} = - (\frac{1}{{(81)}^{\frac{3}{2}}})$

$= - (\frac{1}{{(\sqrt{81})}^{3}})$

$= - (\frac{1}{{(\sqrt{9^{2}})}^{3}})$

$= - \frac{1}{9^{3}}$

$= - \frac{1}{729}$

Part (c) Step 1. Given

An expression ${(- 81)}^{- \frac{3}{2}}$

To simplify the given expression

Part (c) Step 2. Rewrite in radical form and simplify

Rewrite in radical form and simplify

${(- 81)}^{- \frac{3}{2}} = \frac{1}{(- 81)}$ ³³

$= \frac{1}{{(\sqrt{- 81})}^{3}}$

There is no real number whose square root is $- 81$ .

So it has no real root.

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Simplify:
(a) $- 81^{\frac{3}{2}}$ -
(b) $- 81^{- \frac{3}{2}}$
(c) ${(- 81)}^{- \frac{3}{2}}$

Short Answer

Step by step solution

Part (a) Step 1. Given

Part (a) Step 2. Rewrite in radical form and simplify

Part (b) Step 1. Given

Part (b) Step 2. Rewrite in radical form and simplify

Part (c) Step 1. Given

Part (c) Step 2. Rewrite in radical form and simplify

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Simplify:(a)-8132 -(b) -81-32(c) (-81)-32

Short Answer

Step by step solution

Part (a) Step 1. Given

Part (a) Step 2. Rewrite in radical form and simplify

Part (b) Step 1. Given

Part (b) Step 2. Rewrite in radical form and simplify

Part (c) Step 1. Given

Part (c) Step 2. Rewrite in radical form and simplify

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Theoretical and Mathematical Physics

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Statistics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Simplify:
(a) $- 81^{\frac{3}{2}}$ -
(b) $- 81^{- \frac{3}{2}}$
(c) ${(- 81)}^{- \frac{3}{2}}$