# the given expression ( 8 a 6 b 3 2 ) 2 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 65E

(a)

To determine

## To simplify: the given expression (8a6b32)23 .

Expert Solution

(8a6b32)23=4a4b

### Explanation of Solution

Given information:

Given expression

(8a6b32)23

Calculation:

Consider the given expression.

(8a6b32)23

Now, use the law of exponents, which states

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

And combine like terms

(8a6b32)23=823(a6)23(b32)23=(23)23(a6)23(b32)23=(2)3×(23)(a)6×23(b)32×23=22a4b=4a4b

Hence,

(8a6b32)23=4a4b

(b)

To determine

### To simplify: the given expression (4a6b8)32 .

Expert Solution

(4a6b8)32=8a9b12

### Explanation of Solution

Given information:

Given expression

(4a6b8)32

Calculation:

Consider the given expression.

(4a6b8)32

Now, use the law of exponents, which states

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

And combine like terms

(4a6b8)32=432(a6)32(b8)32=(22)32(a6)32(b8)32=(2)2×(32)(a)6×32(b)8×32=23a9b12=8a9b12

Hence,

(4a6b8)32=8a9b12

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