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Adding/Subtracting/Multiplying Exponents when bases are the same Absent Tues/Wed 11/13,14

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To multiply powers with the same base, keep the base and add the exponents. x a x b = x a + b base base = base add exponents 4 5 4 2 = 4 5 + 2 = 4 7 8 3 8 1 = 8 3 + 1 = 8 4

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Example 1 Simplify and write in exponential form (5) 3 (5) 4 (5) 3 + 4 (5) 7 Solution What is exponential form? To re-write the answer with a base(factor) and exponent. What are the bases (factors) of this expression? (5) is the base (factor) of this expression. What are the exponents in this expression? The exponents are 3 & 4 When multiplying and bases are the same what do we do with exponents? We keep the base and add exponents. 5757

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Example #2 Simplify (3x 2 y 3 )(4x 3 y 2 ) 3 4 x 2 + 3 y 3 + 2 12x 5 y 5 Solution What are the coefficients of each monomial? The coefficients are 3 & 4 What do we do with the coefficients? We multiply the coefficients Are there any bases that are the same? Yes or no The x bases are the same and the y bases are the same. When multiplying and the bases are the same what do we do with the exponents? When bases are the same we add exponents. 12x 5 y 5

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To divide powers with the same base, keep the base and subtract the exponents. Basex a = x a - b Basex b 4 5 = 4 5 – 2 = 4 3 4 2 8 3 = 8 3 – 1 = 8 2 8

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Example 3 Simplify the expression and write in exponential form: (-6) 10 (-6) 4 (-6) 10 – 4 (-6) 6 Solution What is exponential form? To re-write the answer with a base(factor) and exponent. What are the bases (factors) of this expression? The base (factor) is (-6) What are the exponents in this expression? The exponents of this expression are 10 & 4. When dividing and bases are the same what do we do with exponents? You keep the base and sub. exponents (-6) 6

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Example 4 Simplify 30c 6 d 5 10c 4 d 3 30 c 6 – 4 d 5 – 3 10 3c 2 d 2 s olution What are the coefficients of each monomial? The coefficients are 30 & 10 What do we do with the coefficients? We divide the coefficients Are there any bases that are the same? Yes or no Both the C & D bases are the same. When dividing and the bases are the same what do we do with the exponents? When dividing and the bases are the same then you sub. The exponents 3c 2 d 2

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To multiply a power to a power, keep the base and multiply the exponents. (x a ) b = x (a)(b) Base exponents (4 5 ) 2 = 4 5(2) = 4 10

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Example 5 Simplify and write in exponential form: (-3 5 ) -2 (-3) (5)(-2) (-3) -10 Solution What is exponential form? To re-write the answer with a base(factor) and exponent. What is the base (factor) of this expression? The base (factor) is (-3) What are the exponents in this expression? The exponents are 5 & -2 When multiplying two powers (exponents) too the same base what do you do with exponents? You keep the base and multiply the exponents (-3) -10

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Example 6 Simplify (3x 2 y 4 ) 3 3 3 x 2(3) y 4(3) 3 3 3 x 6 y 12 9x 6 y 4 Solution What are the factors in this monomial? The factors are 3, x 2, y 4 What do we do first? Draw your arrows What do we do with the exponents? A power(power) you multiply the exponents. Do we re-write this problem? Yes or no We re-write the problem with all the factors multiplied to the 3 rd power. 27x 6 y 12

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