1 Simplifying Exponents

2 Review Multiplication Properties of Exponents Product of Powers Property—To multiply powers that have the same base, ADD the exponents. Power of a Power Property—To find a power of a power, multiply the exponents. Power of a Product Property—To find a power of a product, find the power of each factor and multiply.

3 ANY NUMBER RAISED TO THE FIRST POWER IS ITSELF. FOR EXAMPLE: NOW YOU TRY:

4 Zero Exponents Any number, besides zero, to the zero power is 1. Example:

5 Negative Exponents To make a negative exponent a positive exponent, write it as its reciprocal. In other words, when faced with a negative exponent—make it happy by “flipping” it.

6 Negative Exponent Examples Example of Negative Exponent in the Numerator: The negative exponent is in the numerator— to make it positive, I “flipped” it to the denominator.

7 Negative Exponents Example Negative Exponent in the Denominator: The negative exponent is in the denominator, so I “flipped” it to the numerator to make the exponent positive.

8 Practice Making Negative Exponents Positive 1.Try: 2.Try:

9 Answers to Negative Exponents Practice 1.Answer: 2.Answer:

10 Rewrite the Expression with Positive Exponents Example: Look at EACH factor and decide if the factor belongs in the numerator or denominator. All three factors are in the numerator. The 2 has a positive exponent, so it remains in the numerator, the x has a negative exponent, so we “flip” it to the denominator. The y has a negative exponent, so we “flip” it to the denominator.

11 Rewrite the Expression with Positive Exponents Example: All the factors are in the numerator. Now look at each factor and decide if the exponent is positive or negative. If the exponent is negative, we will flip the factor to make the exponent positive.

12 Rewriting the Expression with Positive Exponents Example: The 4 has a negative exponent so to make the exponent positive— flip it to the denominator. The exponent of a is 1, and the exponent of b is 3—both positive exponents, so they will remain in the numerator. The exponent of c is negative so we will flip c from the numerator to the denominator to make the exponent positive.

13 Practice Rewriting the Expressions with Positive Exponents: 1.Try: 2.Try:

14 Answers 1.Answer 2.Answer

15 Division Properties of Exponents Quotient of Powers Property Power of a Quotient Property

16 Quotient of Powers Property To divide powers that have the same base, subtract the exponents. Example:

17 Practice Quotient of Powers Property 1.Try: 2.Try:

18 Answers 1.Answer: 2.Answer:

19 Power of a Quotient Property To find a power of a quotient, find the power of the numerator and the power of the denominator and divide. Example:

20 Simplifying Expressions Simplify

21 Simplifying Expressions First use the Power of a Quotient Property along with the Power of a Power Property

22 Simplify Expressions Now use the Quotient of Power Property