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5.2 Exponents Objectives The student will be able to: 1. Multiply monomials. 2. Simplify expressions with monomials. 3. Learn and apply the laws of exponents concerning powers of powers.

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A monomial is a 1.number, 2.variable, or 3.a product of one or more numbers and variables. Examples: 5 y 3x 2 y 3

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Why are the following not monomials? x + y addition division 2 - 3a subtraction

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Law of Exponents a m ∙ a n = a m+n

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Multiplying Monomials When multiplying monomials, the base stays the same and you ADD the exponents. 1) x 2 x 4 x x x x 2+4 x6x6

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Multiplying Monomials When multiplying monomials, the base stays the same and you ADD the exponents. 2) 2a 2 y 3 3a 3 y 4 6a 5 y 7

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Simplify m 3 (m 4 )(m) 1.m 7 2.m 8 3.m 12 4.m 13

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Multiplying Monomials When multiplying monomials, the base stays the same and you ADD the exponents. 1) x 13 x 20 x 33 2) 5a 6 y 9 4a 2 y 14 20a 8 y 23

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Law of Exponents (a m ) n = a mn

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When you have an exponent with an exponent, you multiply those exponents. 1) (x 2 ) 3 x 2 3 x6x6 2) (y 3 ) 4 y 12 Power of a Power

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Simplify (p 2 ) 4 1) p 2 2) p 4 3) p 8 4) p 6

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Power of a Product When you have a power outside of the parentheses, everything in the parentheses is raised to that power. (2a) 3 23a323a3 8a38a3 (3x) 2 9x29x2

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Simplify (4r) 3 1.12r 3 2.12r 4 3.64r 3 4.64r 4

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Power of a Monomial 1) (x 3 y 2 ) 4 x 3 4 y 2 4 x 12 y 8 2) (4x 4 y 3 ) 3 64x 12 y 9

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Power of a Monomial What about the order of operations? 3x(2x 2 ) 3 3x ∙ (2 3 x 6 ) 3x ∙ (8x 6 )= 24x 7

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Power of a Monomial What about the order of operations? 5r(3r 3 ) 4 5r ∙ (3 4 r 12 ) 5r ∙ (81r 12 )= 405r 13

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Simplify (3a 2 b 3 ) 4 1.12a 8 b 12 2.81a 6 b 7 3.81a 16 b 81 4.81a 8 b 12

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Assignment 5.2 Worksheet

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