# given expression x 3 y 2 5 x 4 y 16 10 .

### 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 74E

(a)

To determine

## To simplify: given expression x3y25x4y1610 .

Expert Solution

x3y25x4y1610=xy2

### Explanation of Solution

Given information:

Given expression

x3y25x4y1610

Calculation:

Consider the given expression.

x3y25x4y1610

Now, use the law of exponents,

amn=amn and aman=am+n

And combine like terms

x3y25x4y1610=x35x410y25y1610=x35x25y25y85=x35+25y25+85=x3+25y2+85=x55y105=xy2

Hence,

x3y25x4y1610=xy2

(b)

To determine

Expert Solution

8x23x=2x16 .

### Explanation of Solution

Given information:

Given expression

8x23x .

Calculation:

Consider the given expression.

8x23x

Now, use the law of exponents,

amn=amn and aman=amn

And combine like terms

8x23x=813x23x12=(23)13x23x12=2x2312=2x436=2x16

Hence,

8x23x=2x16

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