# given expression 6 y 3 z 2 y z 2 .

### 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 45E

(a)

To determine

## To simplify: given expression 6y3z2yz2 .

Expert Solution

6y3z2yz2=3y2z

### Explanation of Solution

Given information:

Given expression

6y3z2yz2

Calculation:

Consider the given expression.

6y3z2yz2

Now, use the second law of exponents, which states

aman=amn

And combine like terms

6y3z2yz2=62y31z12=3y2z1=3y2z

Hence,

6y3z2yz2=3y2z

(b)

To determine

### To evaluate: the given expression (xy2z3)4(x2y2z)3 .

Expert Solution

(xy2z3)4(x2y2z)3=y2z9x2

### Explanation of Solution

Given information:

Given expression

(xy2z3)4(x2y2z)3

Calculation:

Consider the given expression.

(xy2z3)4(x2y2z)3

Now. Simplify using law of exponents (ab)n=anbn and (am)n=amn .

(xy2z3)4(x2y2z)3={x4(y2)4(z3)4}{(x2)3(y2)3(z)3}=x4y8z12x6y6z3

Now, use the second law of exponents, which states

aman=amn

And combine like terms

x4y8z12x6y6z3=x46y86z123=x2y2z9=y2z9x2

Hence,

(xy2z3)4(x2y2z)3=y2z9x2

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