Bell Work:

• Evaluate each expression:

• 1. 42

• 2. (-2)3

• 3. (1/2)3

• 4. 2 * 1.053

• 5. 34 * 33

Answers:

• 1. 16

• 2. -8

• 3. 1/8

• 4. 2.205

• 5. 2187

Goal:

I can evaluate powers that have zero and negative exponents.

8.2 – Zero and Negative Exponents

Zero and Negative Exponents

Zero and negative exponents are too easy.

DEFINITION OF NEGATIVE EXPONENTS

a-n is the reciprocal of an.

nn

aa

1 , where a is not equal to 0.

What this really means is that you turn a negative exponent into a positive exponent by shifting the power from numerator to denominator or vice versa!

Example

What this really means is that you turn a negative exponent into a positive exponent by shifting the power from numerator to denominator or vice versa!

22

1 12

2 4

33

1 14

4 64

Important – only move the base number and the negative exponent that goes with it!

Examples

a. 3-4 = b. 4-y =

c. d. 0-1 = 1

3

5

Zero and Negative ExponentsZero and negative exponents are too easy.

DEFINITION OF ZERO EXPONENTS

A nonzero number to the zero power has the value of ONE. ANY NUMBER (except zero!) RAISED TO THE ZERO POWER IS ONE!!!!

a0 = 1, where a is not equal to 0.

50 = 1970 = 1

1,000,0000 = 11,5670 = 1

7650 = 1

80 = 11000 = 1

-220 = 1

-40 = 1

-90 = 1

19870 = 1 22.8790 = 1

3000 = 1

More Examples – Rewrite with positive exponents. Assume k is

positive.

a. 4(3-k) = b. 435 hg

More Examples – Evaluate the Expression

a. b. (5-2)-3 =

c. 2-3 =

3 34 4

Examples – Rewrite with positive exponents. Assume n is positive.

a. (4y)-3 = b. ng 2

1

How do you graph an exponential function?To sketch the graph of y = 2x, make a table of values that

includes negative x values……

x -2 -1 0 1 2 3

2x

Next, plot the points on a coordinate plane. What do you notice about the graph?

Safety tips….. Use integer values for x. Base number should always be greater than zero (in this class). In real life applications, x is usally the time period.

Review

Assignment:

Page 459

14 - 48 even