Powers and Exponents

Lesson 14

1. List the following integers from least to greatest: −5, −11, 4, 8, −1, 0

2. Determine the SIGN of each answer.

a. −209 + (− 184) b. −88(45)

c. −244 ÷ −8 d. 2065 − (−6310)

Target: Write and compute expressions with powers.

Power: Used to express a product of a repeated factor. Powers consist of two parts, the base and the exponent.

Base: The repeated factor.

Exponent: Number of times the factor is repeated.

Squared: A number to the second power.

Cubed: A number to the third power.

)3)(3)(3)(3(34 Base

Exponent Repeated Factor

Power Expanded Form

If the base of a power is positive, the value of the power will always be positive.

If the base of a power is negative, the value of the power will be:• positive if the exponent is an even number.• negative if the exponent is an odd number.

Write each expression as a power.

(5)(5)(5)(5)

54

(−11)(−11)

(−11)2

7 ∙ 7 ∙ 7 ∙ 7 ∙ 7 ∙ 7

76

Write each power in expanded form and find its value.

82

8·8 = 64

(−1)5

The exponent is odd so the answer will be negative. (−1)(−1)(−1)(−1)(−1) = −1

Write each power in expanded form and find its value.

−44

Read: “The opposite of four to the fourth power” −(4)(4)(4)(4) = −256

Write each expression as a power.

1. 2∙ 2 ∙ 2 ∙ 2 ∙ 2 ∙ 2

2. (−1)(−1)(−1)

Write each power in expanded form and find the value.

3. 23

4. (−5)2

5. (−3)3

How can you tell the sign of the value of a power without doing any computations?