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Multiplying and Dividing Monomials Absent Monday 11/14

Multiplying and Dividing Monomials Absent Monday 11/14. When multiplying two monomials , you first multiply the coefficients and then add the exponents if bases are the same. ( 6x 2 ) ( 3x 4 ) 6 ● 3 ● x 2 + 4 Coefficients base add exponents 18x 6. Example #1. Simplify

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Multiplying and Dividing Monomials Absent Monday 11/14

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  1. Multiplying and Dividing MonomialsAbsentMonday 11/14

  2. When multiplying two monomials, you first multiply the coefficients and then add the exponents if bases are the same.( 6x2 ) ( 3x4 ) 6 ● 3 ● x2 +4Coefficients base add exponents18x6

  3. Example #1 • Simplify (3x2y3)(4x3y2) 3 ● 4 x2 +3 y3 + 2 • x5 y5 12x5y5 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. 12x5y5

  4. When dividing two monomials, divide the coefficients and if bases are the same subtract the exponents.24y7 3y524 y7–5 3Coefficients base sub. Exponents8y2

  5. Example 2 • Simplify 30c6d5 10c4d3 30 c6–4 d5 – 3 10 3c2d2 solution 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 3c2d2

  6. To raise a monomial to a power (exponent), raise each factor to that power (exponent) and multiply the exponents.(4a3b2)2(4)2 ● (a3)2 ● (b2)2 4 ● 4 (a)3 ● 2 (b)2 ● 2 16 a6 b416a6b4

  7. Example 3 • Simplify (3x2y4)3 33 x2(3) y4(3) 3 ● 3 ● 3 x6 y12 9x6y4Solution What are the factors in this monomial? • The factors are 3, x2, y4 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 3rd power. 27x6y12

  8. Example 4 • Write the expression in expanded form. a3b4 (a)(a)(a) 1 2 3 (b)(b)(b)(b) 1 2 3 4 Solution • What does expanded form mean? • It means to write out all the factors. • How many A’s do I have? • We have three A’s • How many B’s do I have? • We have 4 B’s • Re-write in expanded form. (a)(a)(a)(b)(b)(b)(b)

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