# The expression ( − 3 ) 4 .

### 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, Problem 2T

(a)

To determine

## To evaluate: The expression (−3)4 .

Expert Solution

The value of (3)4 is 81.

### Explanation of Solution

Given:

The expression is (3)4 .

Calculation:

In the given expression 3 is a negative integer and 4 is the exponent of base 3 so the exponential notation of this expression is,

(3)4=(3)(3)(3)(3)=(9)(9)=81

Thus, the value of (3)4 is 81.

(b)

To determine

### To evaluate: The expression −34 .

Expert Solution

The value of 34 is 81 .

### Explanation of Solution

Given:

The expression is 34 .

Calculation:

In the given expression 3 is the positive integer and 4 is the exponent of base 3 so the exponential notation is,

34=(3333)=(81)=81

Thus, the value of 34 is 81 .

(c)

To determine

### To evaluate: The expression 3−4 .

Expert Solution

The value of 34 is 181 .

### Explanation of Solution

Given:

The expression is 34 .

Calculation:

In the given expression 3 is positive integer and 4 is negative exponent of base 3 so by the negative exponents is,

34=134=1(3333)=181

Thus, the value of 34 is 181 .

(d)

To determine

### To evaluate: The expression 523521 .

Expert Solution

The value of 523521 is 25.

### Explanation of Solution

Given:

The expression is 523521 .

Calculation:

The above expression shows that division of two powers of the same number so subtract the exponents,

523521=52321=52=25

Thus, the value of 523521 is 25.

(e)

To determine

### To evaluate: The expression (23)−2 .

Expert Solution

The value of (23)2 is 94 .

### Explanation of Solution

Given:

The expression is (23)2 .

Calculation:

To raise a fraction to a negative power, invert the fraction and change the sign of the exponent in the above expression,

(23)2=(32)2=3322=94

Thus, the value of 523521 is 94 .

(f)

To determine

### To evaluate: The expression 16−3/4 .

Expert Solution

The value of 163/4 is 18 .

### Explanation of Solution

Given:

The expression is 163/4 .

Calculation:

Use exponential law to solve the given expression,

163/4=(161/4)3=(22224)3=(2)3

In the above solution of expression 2 is positive integer and 3 negative exponent so by the negative exponents,

163/4=(2)3=123=1222=18

Thus, the value of 163/4 is 18 .

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