1. Section 8-1: Zero and Negative Exponents
Objectives: (1) To understand that numbers in the real number system are represented in a variety of equivalent forms
(2) To add, subtract, multiply and divide exponential expressions

2. Properties Zero Exponent Property Negative Exponent Property
For every nonzero number a, a0 = 1
Examples
50 = 1 (-2)0 = 1 (-1.02)0 = 1 (1/2)0 = 1
Negative Exponent Property
For every nonzero number a and integer n, a-n=
6-4 = (-8)-1 =

3. Converting Negative Exponents to Positive Exponents
Step 1: Make every number with a negative exponent a fraction (easiest way to convert any number into a fraction is putting it over 1)
Step 2: Move the number to the other side of the fraction bar and change the sign
Step 3: If there are no numbers left on one side of the fraction bar, put a 1 to represent that there was a number there originally.

4. Examples of Converting Negative Exponents
4-3
1 _ 43
1 _____
4 • 4 • 4
1__ This is what we call
simplifying a power

5. Simplifying an Exponential Expression
Simplify the expression 4yx-3 4y X3
Use the definition of negative exponents
Simplify
We’re done!
Tada!

6. Simplifying an Exponential Expression
Simplify the expression: 1 w-4 w4
Move the w to the other side of the fraction bar
You’re done!
Tada!

7. Evaluating Exponential Expressions
Evaulate: 3m2t-2 for t = -3, m = 2 3m2 t2 3(2)2 (-3)2 3(4)
1st: Convert to positive exponents
2nd: Plug in values (put them in parenthesis)
3rd : Simplify
You’re done

8. Real-World Problem Solving
Population Growth:
A biologist is studying green peach aphids (a bug). In the lab, the population doubles every week. The expression 1000 • 2w models an initial population of 1000 insects after w weeks of growth.
Evaluate the expression for w = 0. Then describe what the value of the expression represents in the situation.
Evaluate the expression for w = -3. Then describe what the value of the expression represents in the situation.

9. Part A 1000 • 2w 1000 • 20 1000 • 1 1000 Plug in 0 for w Now evaluate
What does 1000 represent?
The initial number of aphids

10. Part B 1000 • 2w 1000 • 2-3 1000 • 125 Plug in -3 for w Now evaluate
What does 125 represent?
The number of aphids 3 weeks ago