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

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Presentation on theme: "Objective Students will… Solve problems using the laws of exponents."— Presentation transcript:

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.


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