# given expression ( − 2 3 ) − 3 . ### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071 ### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 1.2, Problem 18E

(a)

To determine

## To evaluate: given expression (−23)−3 .

Expert Solution

(23)3=278 .

### Explanation of Solution

Given information:

Given expression

(23)3

Calculation:

Use the fifth law of exponents, which states

(ab)n=anbn(23)3=(2)333

Recall the rule of negative exponents, which states

anbm=bman(2)333=33(2)3

Expand the expression and then multiply.

33(2)3=333222(23)3=278

This is our simplified expression.

(b)

To determine

Expert Solution

(32)2916=14 .

### Explanation of Solution

Given information:

Given expression

(32)2916 .

Calculation:

Use the fifth law of exponents, which states

(ab)n=anbn(32)2916=3222916

Recall the rule of negative exponents, which states

anbm=bman3222=2232

So,

3222916=2232916

Expand the expression and then multiply.

2232916=223391649.916=416=14(32)2916=14

(c)

To determine

### To evaluate: given expression (12)4⋅(52)−2 .

Expert Solution

(12)4(52)2=1100

### Explanation of Solution

Given information:

Given expression

(12)4(52)2

Calculation:

Use the fifth law of exponents, which states

(ab)n=anbn(12)4(52)2=14245222

Recall the rule of negative exponents, which states

anbm=bman14245222=14242252

Expand the expression and then multiply.

14242252=11112222225514242252=4400=1100(12)4(52)2=1100

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