# The expression 4 − 3 2 − 8 , use law of exponents.

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

#### Solutions

Chapter 1.5, Problem 1E

(a)

To determine

## To simplify: The expression 4−32−8 , use law of exponents.

Expert Solution

The expression 4328=4 .

### Explanation of Solution

Law of exponents:

If x and y are positive numbers and m and n are real numbers, then

a.xm+n=xmxnb.xmn=xmxnc.(xm)n=xmnd.(xy)m=xmyn

Calculation:

Use the rule, xa=1xa , and rewrite the expression as 4328=2843 .

Express 4 as a power of 2, 2843=28(22)3 .

Use the law (xm)n=xmn , and simplify as follows.

28(22)3=2826

Then, use the law xmn=xmxn , and simplify further.

2826=286=22=4

Thus, the given expression is simplified as 4328=4 .

(b)

To determine

### To simplify: The expression 1x43 , use law of exponents.

Expert Solution

The expression 1x43=x43 .

### Explanation of Solution

Law of exponents:

If x and y are positive numbers and m and n are real numbers, then

a.xm+n=xmxnb.xmn=xmxnc.(xm)n=xmnd.(xy)m=xmyn

Calculation:

Use the rule, xa=x1a , and rewrite the expression as 1x43=1(x4)13 .

Use the law (xm)n=xmn , and simplify as follows.

1(x4)13=1x43 .

Use the rule, xa=1xa , and rewrite the expression as 1x43=x43 .

Thus, the given expression is simplified as 1x43=x43 .

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