BuyFind

Single Variable Calculus: Concepts...

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

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

Answer to Problem 2E

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

Answer to Problem 2E

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 .

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