# the given expression ( x − 2 3 y 1 2 ) ( x − 2 y − 3 ) 1 6 .

### 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 69E

(a)

To determine

## To simplify: the given expression (x−23y12)(x−2y−3)16 .

Expert Solution

(x23y12)(x2y3)16=1x

### Explanation of Solution

Given information:

Given expression

(x23y12)(x2y3)16

Calculation:

Consider the given expression.

(x23y12)(x2y3)16

Now, use the law of exponents, which states

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

And combine like terms

(x23y12)(x2y3)16=(x23y12)(x2)16(y3)16=(x23y12)x2×16y3×16=(x23y12)x13y12=x2313y1212 [aman=am+n]=x33y0=x1 [a0=1]=1x [an=1an]

Hence,

(x23y12)(x2y3)16=1x

(b)

To determine

### To simplify: the given expression (4y3z23x12)2(x−3y68z4)13 .

Expert Solution

(4y3z23x12)2(x3y68z4)13=8y8x2

### Explanation of Solution

Given information:

Given expression

(4y3z23x12)2(x3y68z4)13

Calculation:

Consider the given expression.

(4y3z23x12)2(x3y68z4)13

Now, use the law of exponents, which states

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

And combine like terms

(4y3z23x12)2(x3y68z4)13=(22)2(y3)2(z23)2(x12)2(x3)13(y6)13(23)13(z4)13=4y6z43xx1y22z43=2y6+2x11 [aman=am+n]=2y8x2=2y8x2 [an=1an]

Hence,

(4y3z23x12)2(x3y68z4)13=8y8x2

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