# given expression ( a 2 a 4 ) 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 39E

(a)

To determine

## To simplify: given expression (a2a4)3 .

Expert Solution

(a2a4)3=a18 .

### Explanation of Solution

Given information:

Given expression

(a2a4)3

Calculation:

Consider the given expression.

(a2a4)3

To simplify this, use the rule of product of exponents, which states

aman=am+n(a2a4)3=(a2+4)3=(a6)3

Now, use (am)n=amn ,

(a2a4)3=(a6)3=a6×3=a18

(b)

To determine

Expert Solution

(a24)3=a664

### Explanation of Solution

Given information:

Given expression

(a24)3 .

Calculation:

Consider the given expression.

(a24)3

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

(ab)n=anbn(a24)3=(a2)343=(a2)364

Now, use the third law of exponents, which states

(am)n=amn(a24)3=(a2)364=a664

(c)

To determine

### To evaluate: given expression (3z)2(6z2)−3 .

Expert Solution

(3z)2(6z2)3=124z4

### Explanation of Solution

Given information:

Given expression

(3z)2(6z2)3

Calculation:

Consider the given expression.

(3z)2(6z2)3

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

(ab)n=anbn(3z)2(6z2)3=(3)2(z)2(6)3(z2)3=9z21666z6 [use(am)n=amn]=z2624 [useam×an=am+n]=124z4 [useam=1am]

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