# given expression ( a 2 b ) 5 ( a 3 b 2 c 3 ) 3 .

### 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 47E

(a)

To determine

## To simplify: given expression (a2b)5(a3b2c3)3 .

Expert Solution

(a2b)5(a3b2c3)3=a19bc9

### Explanation of Solution

Given information:

Given expression

(a2b)5(a3b2c3)3

Calculation:

Consider the given expression.

(a2b)5(a3b2c3)3

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

(a2b)5(a3b2c3)3=(a2)5b5(a3)3(b2)3(c3)3=a10b5a9b6c9

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

aman=am+n,aman=amn

And combine like terms

a10b5a9b6c9=a10+9b65c9=a19bc9=a19bc9

Hence,

(a2b)5(a3b2c3)3=a19bc9

(b)

To determine

### To evaluate: the given expression (u−1v2)2(u3v−2)3 .

Expert Solution

(u1v2)2(u3v2)3=v10u11

### Explanation of Solution

Given information:

Given expression

(u1v2)2(u3v2)3

Calculation:

Consider the given expression.

(u1v2)2(u3v2)3

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

(u1v2)2(u3v2)3=(u1)2(v2)2(u3)3(v2)3=u2v4u9v6

Now, use the second law of exponents, which states

aman=amn

And combine like terms

u2v4u9v6=u29v4(6)=u11v10=v10u11

Hence,

(u1v2)2(u3v2)3=v10u11

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