# given expression ( 5 x 2 y 3 ) ( 3 x 2 y 5 ) 4 .

### 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 43E

(a)

To determine

## To simplify: given expression (5x2y3)(3x2y5)4 .

Expert Solution

(5x2y3)(3x2y5)4=405x10y23

### Explanation of Solution

Given information:

Given expression

(5x2y3)(3x2y5)4

Calculation:

Consider the given expression.

(5x2y3)(3x2y5)4

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

(5x2y3)(3x2y5)4=(5x2y3)34(x2)4(y5)4=(5x2y3)34(x8)(y20)

To simplify this, rewrite the above expression as a single product.

(5x2y3)34(x8)(y20)=534x2x8y3y20=405x2x8y3y20

Now, use the first law of exponents, which states

aman=am+n

And combine like terms

405x2x8y3y20=405x2+8y20+3=405x10y23

Hence,

(5x2y3)(3x2y5)4=405x10y23

(b)

To determine

### To evaluate: the given expression (2a3b2)2(5a2b5)3 .

Expert Solution

(2a3b2)2(5a2b5)3=500a12b19

### Explanation of Solution

Given information:

Given expression

(2a3b2)2(5a2b5)3

Calculation:

Consider the given expression.

(2a3b2)2(5a2b5)3

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

(2a3b2)2(5a2b5)3={22(a3)2(b2)2}{53(a2)3(b5)3}=(4a6b4)(53a6b15)

To simplify this, first rewrite the above expression as a single product.

(4a6b4)(53a6b15)=453a6a6b4b15=500a6a6b4b15

Now, use the first law of exponents, which states

aman=am+n

And combine like terms

500a6a6b4b15=500a6+6b4+15=500a12b19

Hence,

(2a3b2)2(5a2b5)3=500a12b19

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