# The expression b 8 ( 2 b ) 4 , 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 3E

(a)

To determine

## To simplify: The expression b8(2b)4 , use law of exponents.

Expert Solution

The expression b8(2b)4=16b12 .

### 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 b8(2b)4=b8(2)4(b)4 .

Use the law xm+n=xmxn , and simplify as follows.

b8(2)4(b)4=b8(b)4(2)4=b8+4(16)=16b12

Thus, the given expression is simplified as b8(2b)4=16b12 .

(b)

To determine

### To simplify: The expression (6y3)42y5 , use law of exponents.

Expert Solution

The expression (6y3)42y5=648y7 .

### 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 (6y3)42y5=64(y3)42y5 .

Use the law (xm)n=xmn , and simplify such as, 64(y3)42y5=1296y122y5 .

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

1296y72y5=648y125=648y7

Thus, the given expression is simplified as (6y3)42y5=648y7 .

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