# the given expression ( x − 5 y 1 3 ) − 3 5 .

### 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 66E

(a)

To determine

## To simplify: the given expression (x−5y13)−35 .

Expert Solution

(x5y13)35=x3y15

### Explanation of Solution

Given information:

Given expression

(x5y13)35

Calculation:

Consider the given expression.

(x5y13)35

Now, use the law of exponents, which states

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

And combine like terms

(x5y13)35=(x5)35(y13)35=(x)(5)×(35)(y)13×(35)=x3y15=x3y15 [an=1an]

Hence,

(x5y13)35=x3y15

(b)

To determine

### To simplify: the given expression (2x3y−14)2(8y−32)−13 .

Expert Solution

(2x3y14)2(8y32)13=2x6

### Explanation of Solution

Given information:

Given expression

(2x3y14)2(8y32)13

Calculation:

Consider the given expression.

(2x3y14)2(8y32)13

Now, use the law of exponents, which states

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

And combine like terms

(2x3y14)2(8y32)13=22(x3)2(y14)2813(y32)13=4(x3)2(y14)2(23)13(y32)13=4(2)3×(13)(x)3×2(y)2×(14)(y)(32)×(13)=421x6y12y12=2x6y12+12=2x6y0=2x6 [y0=1]

Hence,

(2x3y14)2(8y32)13=2x6

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