# given expression ( s 2 t − 4 5 s − 1 t ) .

### 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 52E

(a)

To determine

## To simplify: given expression (s2t−45s−1t) .

Expert Solution

(s2t45s1t)=s35t5

### Explanation of Solution

Given information:

Given expression

(s2t45s1t)

Calculation:

Consider the given expression.

(s2t45s1t)

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

aman=am+n,aman=amn

And combine like terms

(s2t45s1t)=15s2(1)t41=15s3t5=s35t5

Hence,

(s2t45s1t)=s35t5

(b)

To determine

### To evaluate: the given expression (xy−2z−3x2y3z−4)−3 .

Expert Solution

(xy2z3x2y3z4)3=x3y15z3

### Explanation of Solution

Given information:

Given expression

(xy2z3x2y3z4)3

Calculation:

Consider the given expression.

(xy2z3x2y3z4)3

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

(xy2z3x2y3z4)3=(x)3(y2)3(z3)3(x2)3(y3)3(z4)3=x3y6z9x6y9z12

Now, use the second law of exponents, which states

aman=amn

And combine like terms

x3y6z9x6y9z12=x3(6)y6(9)z912=x3+6y6+9z3=x3y15z3=x3y15z3

Hence,

(xy2z3x2y3z4)3=x3y15z3

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