7.3 MULTIPLICATION AND 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: Remember: An exponent equation has two components: 𝑏 𝑥 Exponent Base

For every number a≠0 and m, n, are integers, Multiplying powers with same base: PROPERTIES: For every number a≠0 and m, n, are integers, 𝑎 𝑚 ∙ 𝑎 𝑛 = 𝑎 𝑚+𝑛 Ex: 1) 41∙ 43 = 41+3 = 44 = 256 = 𝟏 𝟑 𝟐 = 𝟏 𝟗 2) 31 ∙ 3-3 = 31+-3 = 3-2

YOU TRY IT: Simplify: 124 ∙12-2 (-2)5 ∙ (-2)-2 m3 ∙ m-1 ∙ m5 9-3 ∙ 92 ∙ 9-4

SOLUTION: No matter what integer it is, anything to the power of zero is 1. 124 ∙12-2  124-2  122  144 2) (-2)5 ∙ (-2)-2  (-2)5-2  (-2)3  -8 3) m3 ∙ m-1 ∙ m5  m3-1+5  m7  m7 4) 9-3 ∙ 92 ∙ 9-4  𝟏 𝟗 𝟓  9-3+2-4  9-5

For every nonzero number a, b and integer n and m Multiplying and Scientific notation PROPERTIES: For every nonzero number a, b and integer n and m (a×10n)(b×10m) = a∙b×10n+m

EXAMPLE: Simplify: (5×104)(12×10-2 ) (3×10-5)(4×10-2 ) (1.13×10-7)(9.8×105 )(3.34×1022)

SOLUTION: 1) (5×104)(12×10-2 )  (5)(12)× 104-2  60× 102  6.0× 103 2) (3×10-5)(4×10-2 )  (3)(4)× 10-5-2  12× 10-7  1.2× 10-6 3) (1.13×10-7)(9.8×105 )(3.34×1022)  (1.13)(9.8)(3.34)× 10-7+5+22  36.99× 1020  3.699× 1021

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

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

𝑎 −𝑛 = 1 𝑎 𝑛 Ex: 2) (-3)-2 = 𝟏 (−𝟑)𝟐 = 𝟏 𝟗 1) 4-1 = 𝟏 𝟒 PROPERTIES: Negative numbers: as an exponents For every nonzero number a≠0, and integer n 𝑎 −𝑛 = 1 𝑎 𝑛 Ex: 2) (-3)-2 = 𝟏 (−𝟑)𝟐 = 𝟏 𝟗 1) 4-1 = 𝟏 𝟒

For every number a≠0 and m, n, are integers, Multiplying powers with same base: PROPERTIES: For every number a≠0 and m, n, are integers, 𝑎 𝑚 ∙ 𝑎 𝑛 = 𝑎 𝑚+𝑛 Ex: 1) 41∙ 43 = 41+3 = 44 = 256 2) 31 ∙ 3-3 = 31+-3 = 3-2 = 𝟏 𝟑 𝟐 = 𝟏 𝟗

For every nonzero number a, b and integer n and m Multiplying and Scientific notation PROPERTIES: For every nonzero number a, b and integer n and m (a×10n)(b×10m) = a∙b×10n+m

Exponents and Multiplication VIDEOS: Exponents and Multiplication https://www.khanacademy.org/math/algebra/exponent-equations/exponent-properties-algebra/v/exponent-properties-involving-products https://www.khanacademy.org/math/algebra/exponent-equations/exponent-properties-algebra/v/rational-exponents-and-exponent-laws

CLASSWORK: Page 424: Problems: As many as needed to master the concept. Page: 429: Problems: As many as needed to master the