# given expression z 2 z 4 z 3 z − 1 . ### 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 38E

(a)

To determine

## To simplify: given expression z2z4z3z−1 .

Expert Solution

z2z4z3z1=z4 .

### Explanation of Solution

Given information:

Given expression

z2z4z3z1

Calculation:

Consider the given expression.

z2z4z3z1

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

aman=am+nz2z4z3z1=z6z2

Now, use the second law of exponents, which states

aman=amnz6z2=z62z6z2=z4z2z4z3z1=z4

(b)

To determine

Expert Solution

(2y2)3=8y6

### Explanation of Solution

Given information:

Given expression

(2y2)3 .

Calculation:

Consider the given expression.

(2y2)3

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

(ab)n=anbn(2y2)3=(2)3(y2)3(2y2)3=8(y2)3

Now, use the third law of exponents, which states

(am)n=amn8(y2)3=8y238(y2)3=8y6(2y2)3=8y6

(c)

To determine

Expert Solution

(8x)2=64x2

### Explanation of Solution

Given information:

Given expression

(8x)2

Calculation:

Consider the given expression.

(8x)2

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

(ab)n=anbn(8x)2=(8)2(x)2(8x)2=64x2

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