# The expression 8 4 3 , 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 2E

(a)

To determine

## To simplify: The expression 843 , use law of exponents.

Expert Solution

The expression 843=16 .

### 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 law (xm)n=xmn , and rewrite the expression as 843=(813)4 .

Then, use the rule, xa=x1a , and simplify as follows.

843=(83)4=24=16

Thus, the given expression is simplified as 843=16 .

(b)

To determine

### To simplify: The expression x(3x2)3 , use law of exponents.

Expert Solution

The expression x(3x2)3=27x7 .

### 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 law (xy)m=xmyn , and rewrite the expression as x(3x2)3=x(3)3(x2)3 .

Use the law (xm)n=xmn , and simplify such as, x(3)3(x2)3=27x(x)6 .

Then, use the law xm+n=xmxn , and simplify further as, 27x(x)6=27x7 .

Thus, the given expression is simplified as x(3x2)3=27x7 .

### 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!