# given expression 8 a 3 b − 4 2 a − 5 b 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 49E

(a)

To determine

## To simplify: given expression 8a3b−42a−5b5 .

Expert Solution

8a3b42a5b5=4a8b9

### Explanation of Solution

Given information:

Given expression

8a3b42a5b5

Calculation:

Consider the given expression.

8a3b42a5b5

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

aman=am+n,aman=amn

And combine like terms

8a3b42a5b5=82a3(5)b45=4a3+5b9=4a8b9=4a8b9

Hence,

8a3b42a5b5=4a8b9

(b)

To determine

### To evaluate: the given expression (y5x−2)−3 .

Expert Solution

(y5x2)3=125x6y3

### Explanation of Solution

Given information:

Given expression

(y5x2)3

Calculation:

Consider the given expression.

(y5x2)3

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

(y5x2)3=y353(x2)3=y353x6

Now, use the second law of exponents, which states

aman=amn

And combine like terms

y353x6=y3(53)1x6=53x6y3=125x6y3

Hence,

(y5x2)3=125x6y3

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