# given expression x − 5 x 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 36E

(a)

To determine

## To simplify: given expression x−5x3 .

Expert Solution

x5x3=1x2 .

### Explanation of Solution

Given information:

Given expression

x5x3

Calculation:

Consider the given expression.

x5x3

To simplify this, we will use the first law of exponents, which states

aman=am+nx5x3=x5+3x5x3=x2

Use the rule of negative exponents, which states

an=1anx2=1x2x5x3=1x2

This is our simplified expression.

(b)

To determine

Expert Solution

w2w4w6=1

### Explanation of Solution

Given information:

Given expression

w2w4w6 .

Calculation:

Consider the given expression.

w2w4w6

To simplify this, we will use the first law of exponents, which states

amanap=am+n+pw2w4w6=w(2)+(4)+6w2w4w6=w0

Use the rule of zero exponents, which states

a0=1w2w4w6=w0=1

This is our simplified expression.

(c)

To determine

Expert Solution

z5z3z4=1z2

### Explanation of Solution

Given information:

Given expression

z5z3z4

Calculation:

Consider the given expression.

z5z3z4

To simplify this, we will use the first law of exponents, which states

aman=am+nz5z3z4=z5+(3)+(4)z5z3z4=z2

Use the rule of negative exponents, which states

an=1anz2=1z2z5z3z4=1z2

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