# Zero and Negative Exponents Worksheet

Zero and Negative Exponents Worksheet
• Page 1
1.
Evaluate the expression.
5 - 3 × 55
 a. 25 b. 125 c. $\frac{1}{25}$ d. $\frac{1}{125}$

#### Solution:

5 - 3 × 55 = 5 - 3 + 5
[Use the product of powers property.]

= 52

= 25
[Evaluate the power.]

The value of the expression is 25.

Correct answer : (1)
2.
Evaluate the expression.
3- 4 × 30
 a. $\frac{1}{27}$ b. $\frac{1}{81}$ c. 81 d. 27

#### Solution:

3- 4 × 30 = 3- 4 + 0
[Use the product of powers property.]

= 3- 4

= 1(3)4
[Use the negative exponent definition.]

= 1 / 81
[Evaluate the power.]

The value of the expression is 1 / 81.

Correct answer : (2)
3.
Evaluate the expression: (- 3) - 4
 a. - 81 b. 81 c. $\frac{1}{81}$ d. - $\frac{1}{81}$

#### Solution:

(- 3)- 4 = 1(- 3)4
[Use the rules for negative exponents.]

= 1 / 81
[Negative number raised to the even power gives positive number.]

The value of the expression is 1 / 81.

Correct answer : (3)
4.
10 - 4 = _______
 a. - $\frac{1}{10005}$ b. $\frac{1}{10003}$ c. $\frac{1}{10000}$ d. - $\frac{1}{10000}$

#### Solution:

10 - 4 = 1104
[Use the rules for negative exponents.]

= 110000

Correct answer : (3)
5.
Evaluate the expression 2 - 3.
 a. 8 b. 4 c. $\frac{1}{8}$ d. $\frac{1}{4}$

#### Solution:

2- 3
[Original expression.]

= 1(2)3
[Use the rules for negative exponents.]

= 1 / 8
[Evaluate the power.]

The value of the expression is 1 / 8.

Correct answer : (3)
6.
Evaluate the expression.
(- 2 × 3)- 2 + 2
 a. $\frac{1}{36}$ b. 32 c. 36 d. {s1}

Correct answer : (4)
7.
Evaluate the expression: (- 3) - 2
 a. 9 b. $\frac{1}{9}$ c. - $\frac{1}{9}$ d. - 9

#### Solution:

(- 3)- 2 = 1(- 3)2
[Use the rules for negative exponents.]

= 1 / 9
[Negative number raised to the even power gives positive number.]

The value of the expression is 1 / 9.

Correct answer : (2)
8.
Evaluate the expression.
(3 × 4)- 3
 a. $\frac{1}{1792}$ b. $\frac{1}{1728}$ c. 1792 d. 1728

#### Solution:

(3 × 4)- 3 = 1(3 × 4)3
[Use definition of negative exponents.]

= 133×43
[Use power of product property.]

= 127 × 64
[Evaluate the powers.]

= 1 / 1728
[Multiply.]

The value of the expression is 1 / 1728.

Correct answer : (2)
9.
Evaluate the expression.
(- 4)- 6 × (- 4)4
 a. $\frac{1}{4}$ b. 16 c. $\frac{1}{16}$ d. 4

#### Solution:

(- 4)- 6 × (- 4)4 = (- 4)- 6 + 4
[Use the product of powers property.]

= (- 4)- 2

= 1(- 4)2
[Use the negative exponent definition.]

= 116
[Evaluate the power.]

The value of the expression is 1 / 16.

Correct answer : (3)
10.
Which one of the following is another way of writing the expression 6$n$- 6?
 a. $\frac{6}{{n}^{6}}$ b. 6$n$6 c. d. (- 6)$n$6

#### Solution:

6n- 6 = 6 × 1n6
[Use the rules for negative exponents.]

= 6n6
[Simplify.]

So, another way of writing the expression 6n- 6 is 6n6.
[Rewrite the expression with positive exponents.]

Correct answer : (1)

*AP and SAT are registered trademarks of the College Board.