1 Simplifying Exponents

Likewise, 5 · 5 · 5 · 5 = 5 4, because there are four 5’s being multiplied together. Power – a number produced by raising a base to an exponent. (the term 2 7 is called a power.) Exponential form – a number written with a base and an exponent. (2 3 ) Exponent – the number that indicates how many times the base is used as a factor. (2 7 ) Base – when a number is being raised to a power, the number being used as a factor. (2 7 )

Example Power Means: Exponent Base

4 Multiplication Properties of Exponents Product of Powers Property Power of a Power Property Power of a Product Property

5 Product of Powers Property To multiply powers that have the same base, you add the exponents. Example:

6 Practice Product of Powers Property: Try:

7 Power of a Power Property To find a power of a power, you multiply the exponents. Example: Therefore,

8 Practice Using the Power of a Power Property 1.Try: 2.Try:

9 Power of a Product Property To find a power of a product, find the power of EACH factor and multiply. Example:

10 Practice Power of a Product Property 1.Try: 2.Try:

11 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.

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

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

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