# 7.1 Exponent Properties Involving Products

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7.1 Exponent Properties Involving Products
At-Home Lesson 7.1 Exponent Properties Involving Products

Math Standards Technology Standards
NS Multiply, divide, and simplify rational numbers by using exponent rules. AF Simplify and evaluate expressions that include exponents. Technology Standards 5a - Advocate and practice safe, legal, and responsible use of information and technology. 6b - Select and Use applications effectively and productively.

Review Exponent 3 X

Review 3 X Base

The exponent and the base together are called...Power.
Review 3 X The exponent and the base together are called...Power.

Definition of a negative exponent
Review Definition of a negative exponent 1 a -n = a n

Exponent Properties Involving Products
Section 7.1

. a a a = Review Product of Powers Property m n m + n
To multiply powers with the same base, add their exponents.

Product of Powers Property
Using the... Product of Powers Property Example A . 8 9 8 + 9 7 7 = 7 Product of powers property 7 17 = Add Exponents

Product of Powers Property
Using the... Product of Powers Property Example B . x x x 7 4 7 + 4 = Product of powers property x 17 = Add Exponents

Product of Powers Property
Using the... Product of Powers Property Example C . y y y -2 -5 -2 + (-5) = Product of powers property y -7 = Add Exponents Definition of negative exponent = 1 y 7

a a ( ) = Review Power of a Power Property m n m n
To simplify a power of a power, multiply exponents.

Power of a Power Property
Using the... Power of a Power Property Example A 6 ( ) . 4 4 4 4 = Power of a power property 6 16 = Multiply Exponents 6

Power of a Power Property
Using the... Power of a Power Property Example B [ ] -0.3 -0.3 ( ) ( ) . 5 2 5 2 = Power of a power property -0.3 ( ) 10 Multiply Exponents =

Power of a Power Property
Using the... Power of a Power Property Example C m ( ) . -3 4 -3 4 = Power of a power property m = Multiply Exponents -12 m = 1 Definition of negative exponents m 12

( ab ) a b = Review Power of a Product Property m m m
To simplify a power of a product, find the power of each factor and multiply.

Power of a Product Property
Using the... Power of a Product Property Example A 3x ( ) 4 4 4 = Power of a product property 3 x = 4 Evaluate power 81x

Power of a Product Property
Using the... Power of a Product Property Example B -4d -4 d -3 -3 -3 ( ) ( ) = . Power of a product property 1 1 Definition of negative exponent = -4 d . ( ) 3 3 Continued

Power of a Product Property
Using the... Power of a Product Property Example B continued 1 1 = -64 d Evaluate Power . ( ) 3 3 1 Simplify = - 64 d 3

At-Home Quiz* (You may use the previous examples for help)
*Work needs to be turned in first thing tomorrow

Quiz . x x 4z ( ) 7 4 4 a) b) y rs ( ) ( ) 2 -5 9 c) d)

At-Home Quiz is now complete
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