# given expression 5 x y − 2 x − 1 y − 3 .

### 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 50E

(a)

To determine

## To simplify: given expression 5xy−2x−1y−3 .

Expert Solution

5xy2x1y3=5x2y

### Explanation of Solution

Given information:

Given expression

5xy2x1y3

Calculation:

Consider the given expression.

5xy2x1y3

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

aman=am+n,aman=amn

And combine like terms

5xy2x1y3=5x1(1)y2(3)=5x1+1y2+3=5x2y1=5x2y

Hence,

5xy2x1y3=5x2y

(b)

To determine

### To evaluate: the given expression (2a−1ba2b−3)−3 .

Expert Solution

(2a1ba2b3)3=a98b12

### Explanation of Solution

Given information:

Given expression

(2a1ba2b3)3

Calculation:

Consider the given expression.

(2a1ba2b3)3

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

(2a1ba2b3)3=23(a1)3b3(a2)3(b3)3=a3b323a6b9

Now, use the second law of exponents, which states

aman=amn

And combine like terms

a3b323a6b9=18a3(6)b39=18a3+6b12=a98b12

Hence,

(2a1ba2b3)3=a98b12

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