# given expression ( 3 a b 3 ) − 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 51E

(a)

To determine

## To simplify: given expression (3ab3)−1 .

Expert Solution

(3ab3)1=b33a

### Explanation of Solution

Given information:

Given expression

(3ab3)1

Calculation:

Consider the given expression.

(3ab3)1

Now, use the first and second law of exponents, which states

aman=am+n,aman=amn

And combine like terms

(3ab3)1=31a1b3=13ab3=b33a

Hence,

(3ab3)1=b33a

(b)

To determine

### To evaluate: the given expression (q−1r−1s−2r−5sq−8)−1 .

Expert Solution

(q1r1s2r5sq8)1=s3q7r4

### Explanation of Solution

Given information:

Given expression

(q1r1s2r5sq8)1

Calculation:

Consider the given expression.

(q1r1s2r5sq8)1

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

(q1r1s2r5sq8)1=(q1)1(r1)1(s2)1(q8)1(r5)1(s)1=qrs2q8r5s1

Now, use the second law of exponents, which states

aman=amn

And combine like terms

qrs2q8r5s1=q18r15s2(1)=q7r4s3=s3q7r4

Hence,

(q1r1s2r5sq8)1=s3q7r4

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