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Chapter 8: Q. 8.57 (page 777)

Simplify:

(a)(-64)-12

(b) -6412

(c) (64)-12

Short Answer

Expert verified

The simplification of (-64)-12 is no real root

The simplification of -6412is-8

The simplification of (64)-12is 18

Step by step solution

01

Part (a) Step 1. Given

The expression is (-64)12

To simplify the expression.

02

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

Rewrite using the property, a-n=1an,

(-64)-12=1(-64)12
Rewrite as the square root

It cannot be written as perfect square root.

So it has no real root.

03

Part (b) Step 1. Given

The expression is -6412

To simplify the expression.

04

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

Rewrite as the square root

-6412

The root is only for 64. So,

-6412=-(82)12

=-8

05

Part (c) Step 1. Given

The expression is (64)-12

To simplify the expression.

06

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

Rewrite using the property, a-n=1an

(64)-12=16412

Rewrite as the square root

=1(82)12

=18

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