7.1 Zero and Negative Exponents: Base: A number that is multiplied repeatedly. Exponent: A number that shows repeated multiplication. Property: A character or attribute that something has.

GOAL:

An exponent equation has two components: Definition: An exponent equation has two components: 𝑏 𝑥 Exponent Base

𝑎 0 = 1 For every number a, Ex: 40 = 1 (-3)0 = 1 1000 = 1 ZERO: as an exponent PROPERTIES: For every number a, 𝑎 0 = 1 Ex: 40 = 1 (-3)0 = 1 1000 = 1 1,000,0000 = 1 (-½) 0 = 1

Simplify the following exponents: YOU TRY IT: Simplify the following exponents: -1 0 (-1) 0 m 0 -1/3 0

-1 0 = -1 (-1) 0 = 1 m 0 = 1 -1/3 0 = -1 SOLUTION: No matter what integer it is, anything to the power of zero is 1. -1 0 = -1 (-1) 0 = 1 m 0 = 1 -1/3 0 = -1

𝑎 −𝑛 = 1 𝑎 𝑛 For every nonzero number a and integer n Negative numbers: as an exponents PROPERTIES: For every nonzero number a and integer n 𝑎 −𝑛 = 1 𝑎 𝑛

NOTE: In math we never like to work with negative exponents. We must always provide answers with positive exponents. Ex:  1 3 2  1 9 3 −2  − 1 2 2  − 1 4 −2 −2

1 3 −2 1( 3 +2 ) 1(9) = 9 6 2 −2 6( 2 +2 ) 6(4) =24 Ex: ALSO: If negative exponents are in the denominator, we still turn them into positive. Ex: 1 3 −2 1( 3 +2 ) 1(9) = 9 6 2 −2 6( 2 +2 ) 6(4) =24

b) 1 𝑥 −5 a)5a3b-2 d) 𝑛 −2 𝑚 −5 c)4c-3r SIMPLIFYING EXPONENTIAL EXPRESSIONS: Once again, always give answers with positive exponents only! Ex: What is the simplified form of each expression? b) 1 𝑥 −5 a)5a3b-2 d) 𝑛 −2 𝑚 −5 c)4c-3r

 5𝑎3 𝑏 2 a)5a3b-2 b) 1 𝑥 −5  x5  4𝑟 𝑐 3 c) 4c-3r d) 𝑛 −2 𝑚 −5 SOLUTIONS: Switch the integers that have negative to the other side.  5𝑎3 𝑏 2 a)5a3b-2 b) 1 𝑥 −5  x5  4𝑟 𝑐 3 c) 4c-3r d) 𝑛 −2 𝑚 −5  𝑚5 𝑛 2

VIDEO: Get a hot chocolate and enjoy this!!!. Exponents Definition http://www.khanacademy.org/math/algebra/exponent-equations/exponent-properties-algebra/v/exponent-properties-1 Negative Exponents http://www.khanacademy.org/math/algebra/exponent-equations/exponent-properties-algebra/v/exponent-properties-2 Negative and Positive Exponents http://www.khanacademy.org/math/algebra/exponent-equations/exponent-properties-algebra/v/negative-and-positive-exponents

CLASSWORK: Page 417-418: Problems: As many as needed to understand the concept