# given expression ( 2 z 2 ) − 5 z 10 .

### 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 40E

(a)

To determine

## To evaluate: given expression (2z2)−5z10 .

Expert Solution

(2z2)5z10=132

### Explanation of Solution

Given information:

Given expression

(2z2)5z10

Calculation:

Consider the given expression.

(2z2)5z10

To simplify this, use the fourth law of exponents, which states

(ab)n=anbn(2z2)5z10=(2)5(z2)5z10=132z10z10 [use(am)n=amn]=z10+1032 [useam×an=am+n]=132 [useam=1am]

(b)

To determine

Expert Solution

(2a3a2)4=16a20

### Explanation of Solution

Given information:

Given expression

(2a3a2)4

Calculation:

Consider the given expression.

(2a3a2)4

To simplify this, use the fifth law of exponents, which states

(ab)n=anbn(2a3a2)4=(2)4(a3)4(a2)4 =16a12a8 [Use(am)n=amn]=16a8+12 [Useaman=am+n]=16a20

(c)

To determine

### To evaluate: given expression (3x44x2)2 .

Expert Solution

(3x44x2)2=916x4

### Explanation of Solution

Given information:

Given expression

(3x44x2)2

Calculation:

Consider the given expression.

(3x44x2)2

To simplify this, use the fourth law of exponents, which states

(ab)n=anbn(3x44x2)2=(3)2(x4)2(4)2(x2)2=9x816x4 [use(am)n=amn]=9x8416 [useam×an=am+n]=9x416 [useam=1am]

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