Chapter 8: Q. 8.57 (page 777)

Simplify:
(a) ${(- 64)}^{- \frac{1}{2}}$
(b) ${- 64}^{\frac{1}{2}}$
(c) ${(64)}^{- \frac{1}{2}}$

Short Answer

Expert verified

The simplification of ${(- 64)}^{- \frac{1}{2}}$ is no real root

The simplification of $- 64^{\frac{1}{2}}$ is $- 8$

The simplification of ${(64)}^{- \frac{1}{2}}$ is $\frac{1}{8}$

Step by step solution

Part (a) Step 1. Given

The expression is ${(- 64)}^{\frac{1}{2}}$

To simplify the expression.

Part (a) Step 2. Rewrite as the nth root

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

${(- 64)}^{\frac{- 1}{2}} = \frac{1}{{(- 64)}^{\frac{1}{2}}}$
Rewrite as the square root

It cannot be written as perfect square root.

So it has no real root.

Part (b) Step 1. Given

The expression is $- 64^{\frac{1}{2}}$

To simplify the expression.

Part (b) Step 2. Rewrite as the nth root

Rewrite as the square root

$- 64^{\frac{1}{2}}$

The root is only for $64$ . So,

$- 64^{\frac{1}{2}} = - {(8^{2})}^{\frac{1}{2}}$

$= - 8$

Part (c) Step 1. Given

The expression is ${(64)}^{- \frac{1}{2}}$

To simplify the expression.

Part (c) Step 2. Rewrite as the nth root

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

${(64)}^{- \frac{1}{2}} = \frac{1}{64}$ ¹²

Rewrite as the square root

$= \frac{1}{{(8^{2})}^{\frac{1}{2}}}$

$= \frac{1}{8}$

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Simplify:
(a) ${(- 64)}^{- \frac{1}{2}}$
(b) ${- 64}^{\frac{1}{2}}$
(c) ${(64)}^{- \frac{1}{2}}$

Short Answer

Step by step solution

Part (a) Step 1. Given

Part (a) Step 2. Rewrite as the nth root

Part (b) Step 1. Given

Part (b) Step 2. Rewrite as the nth root

Part (c) Step 1. Given

Part (c) Step 2. Rewrite as the nth root

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Simplify:(a)(-64)-12(b) -6412(c) (64)-12

Short Answer

Step by step solution

Part (a) Step 1. Given

Part (a) Step 2. Rewrite as the nth root

Part (b) Step 1. Given

Part (b) Step 2. Rewrite as the nth root

Part (c) Step 1. Given

Part (c) Step 2. Rewrite as the nth root

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

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Mechanics Maths

Study anywhere. Anytime. Across all devices.

Simplify:
(a) ${(- 64)}^{- \frac{1}{2}}$
(b) ${- 64}^{\frac{1}{2}}$
(c) ${(64)}^{- \frac{1}{2}}$