# the given expression ( x 8 y − 4 16 y 4 3 ) − 1 4 .

BuyFind

### Precalculus: Mathematics for Calcu...

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

### Precalculus: Mathematics for Calcu...

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

#### Solutions

Chapter 1.2, Problem 68E

(a)

To determine

Expert Solution

## Answer to Problem 68E

(x8y416y43)14=2y43x2

### Explanation of Solution

Given information:

Given expression

(x8y416y43)14

Calculation:

Consider the given expression.

(x8y416y43)14

Now, use the law of exponents, which states

(am)n=amn , (ab)n=anbn and (ab)n=anbn

And combine like terms

(x8y416y43)14=(x8)14(y4)14(24)14(y43)14=(x)8×(14)(y)(4)×(14)(2)4×(14)(y)43×(14)=x2y21y13=2y43x2 [an=1an]

Hence,

(x8y416y43)14=2y43x2

(b)

To determine

Expert Solution

## Answer to Problem 68E

(8y34y3z6)13=y34z22

### Explanation of Solution

Given information:

Given expression

(8y34y3z6)13

Calculation:

Consider the given expression.

(8y34y3z6)13

Now, use the law of exponents, which states

(am)n=amn , (ab)n=anbn and (ab)n=anbn

And combine like terms

(8y34y3z6)13=(23)13(y34)13(y3)13(z6)13=(2)3×(13)(y)34×(13)(y)3×(13)(z)6×(13)=21y14y1z2=12×y114×z2 =y34z22

Hence,

(8y34y3z6)13=y34z22

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