1. Objective
Students will…
Solve problems using the laws of exponents.

2. Laws of Exponents
In order for the laws of exponents to work, the bases have to be the same!
There are three laws of exponents we will learn today.

3. Introduction
How would you find 22 * 23?
What is 25?

4. Product of Powers
What is the rule for finding a product of powers? *When bases are being multiplied add the exponents together.
When you have a product of powers, just add the exponents together.
Example:
x2 * x12 = x*x*x*x*x*x*x*x*x*x*x*x*x*x =x14 or x2 * x12 = x2+12 = x14

5. Product of Powers Simplify the problems to be written as a power.
109 * 104
72 * 75
x2 * x12

6. Power of a Power How would we simplify a power of a power?
To raise a power to a power, we multiply the exponents.
Example: (25)3 = 215

7. Power of Powers
Simplify the problem to be written as a power.
(h2)4

8. Quotient of Powers
How would we simplify the following problem?

9. Quotient of Powers What is the rule for finding a quotient of powers?
When dividing, we subtract the exponents if the bases are the same.
Example: 25
23 = 22

10. Negative Exponents
Powers with negative exponents can be written as a fraction, with 1 as the numerator and the power with a positive exponent as the denominator.
Example:

11. Examples
Write each expression with a positive exponent.

12. Challenge
Simplify the example below.