given expression − 3 2 .

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 15E

(a)

To determine

To evaluate: given expression −32 .

Expert Solution

9

Explanation of Solution

Given information:

Given expression

32

Calculation:

We want to evaluate

32

Because there are no parentheses, evaluate the exponent first, and then multiply by 1 . That is, we should first rewrite our expression as

32=(32)

By the definition of exponential notation, which states that

an=aaaanfactorsan=aaaanfactors,

We can say that 32 is simply 3 multiplied by itself 2 times.

32=3332=9

Now, put this back into our original expression and we get,

32=(32)32=(9)32=9

(b)

To determine

Expert Solution

(3)2=9

Explanation of Solution

Given information:

Given expression

(3)2 .

Calculation:

Because of the parentheses, the power is applied to 3 . By the definition of exponential notation, which states that,

an=aaaanfactorsan=aaaanfactors,

The expression simply represents 3 multiplied by itself 2 times.

(3)2=(3)(3)(3)2=9

(c)

To determine

To evaluate: given expression (13)4(−3)2 .

Expert Solution

(13)4(3)2=(19) .

Explanation of Solution

Given information:

Given expression

(13)4(3)2

Calculation:

Consider the expression

(13)4(3)2

Here, we will again use the definition of exponential notation. Recall that this states

an=aaaanfactorsan=aaaanfactors,

Expand the expression into the multiplication it represents.

(13)4(3)2=(13)(13)(13)(13)(3)(3)=(181)(9)=(19)

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