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

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.

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

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

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

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

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

Quotient of Powers How would we simplify the following problem?

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

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:

Examples Write each expression with a positive exponent.

Challenge Simplify the example below.