# given expression ( x 4 z 2 4 y 5 ) ( 2 x 3 y 2 z 3 ) 2 . ### 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 48E

(a)

To determine

## To simplify: given expression (x4z24y5)(2x3y2z3)2 .

Expert Solution

(x4z24y5)(2x3y2z3)2=x10yz4

### Explanation of Solution

Given information:

Given expression

(x4z24y5)(2x3y2z3)2

Calculation:

Consider the given expression.

(x4z24y5)(2x3y2z3)2

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

(x4z24y5)(2x3y2z3)2=(x4z24y5)22(x3)2(y2)2(z3)2=(x4z24y5)4x6y4z6

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

aman=am+n,aman=amn

And combine like terms

(x4z24y5)4x6y4z6=44x4+6z26y45=x10z4y1=x10yz4

Hence,

(x4z24y5)(2x3y2z3)2=x10yz4

(b)

To determine

### To evaluate: the given expression (rs2)3(r−3s2)2 .

Expert Solution

(rs2)3(r3s2)2=r9s2

### Explanation of Solution

Given information:

Given expression

(rs2)3(r3s2)2

Calculation:

Consider the given expression.

(rs2)3(r3s2)2

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

(rs2)3(r3s2)2=(r)3(s2)3(r3)2(s2)2=r3s6r6s4

Now, use the second law of exponents, which states

aman=amn

And combine like terms

r3s6r6s4=r3(6)s64=r3+6s2=r9s2

Hence,

(rs2)3(r3s2)2=r9s2

### Have a homework question?

Subscribe to bartleby learn! Ask subject matter experts 30 homework questions each month. Plus, you’ll have access to millions of step-by-step textbook answers!