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Chapter 8: Q 135E (page 786)

In the following exercises, simplify.

Part (a):-8114

Part (b): -8114

Part (c): 81-14

Short Answer

Expert verified

Part (a): On simplifying, we know the solution is not real.

Part (b): On simplifying, we get -3.

Part (c): On simplifying, we get 13.

Step by step solution

01

Part (a) Step 1. Rewrite as a root.

Consider the given question,

-8114

Rewrite as a fourth root,

=-814

On simplifying the expression,

localid="1644769902253" =-344

The solution is not real.

02

Part (b) Step 1. Rewrite as a root.

Consider the given question,

-8114

The exponent only applies to the 81.

Rewrite as a fourth root,

=-814

On simplifying the expression,

=-344=-3

03

Part (c) Step 1. Rewrite as a root.

Consider the given question,

81-14

Rewrite using the property a-n=1an,

=18114

Rewrite as a fourth root,

=1814

On simplifying the expression,

=1344=13

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