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# Multiplying Monomials

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### Multiplying Monomials

1. 1. MonomialsMultiplying Monomials and Raising Monomials to Powers
2. 2. Vocabulary• Monomials - a number, a variable, or a product of a number and one or more variables • 4x, 20x2yw3, -3, a2b3, and 3yz are all monomials.• Constant – a monomial that is a number without a variable.• Base – In an expression of the form xn, the base is x.• Exponent – In an expression of the form xn, the exponent is n.
3. 3. Writing - Using ExponentsRewrite the following expressions using exponents: x x x x y yThe variables, x and y, represent the bases. Thenumber of times each base is multiplied by itself willbe the value of the exponent. 4 2 x x x x y y x y
4. 4. Writing Expressions without ExponentsWrite out each expression without exponents (asmultiplication): 3 2 8a b 8 a a a b b 4 xy xy xy xy xy or x x x x y y y y
5. 5. Product of Powers Simplify the following expression: (5a2)(a5) There are two monomials. Underline them. What operation is between the two monomials? Multiplication !Step 1: Write out the expressions in expanded form. 2 5 5a a 5 a a a a a a aStep 2: Rewrite using exponents. 2 5 7 7 5a a 5 a 5a
6. 6. Product of Powers RuleFor any number a, and all integers m and n, am • an = am+n. 9 4 13 1) a a a 2 10 12 2) w w w 5 6 3) r r r 5 3 8 4) k k k 2 2 2 2 5) x y x y
7. 7. Multiplying MonomialsIf the monomials have coefficients, multiplythose, but still add the powers. 9 4 13 1) 4a 2a 8a 2 10 12 2) 7w 10w 70w 5 6 3) 2r 3r 6r 5 3 8 4) 3k 7k 21k 2 2 2 2 5) 12 x 2y 24x y
8. 8. Multiplying MonomialsThese monomials have a mixture ofdifferent variables. Only add powers of likevariables. 9 3 4 13 4 1) 4a b 2a b8a b 2 5 10 2 12 7 2) 7w y 10 w y 70w y 3 5 6 3 3) 2rt 3r 6r t 5 4 3 3 3 8 4 7 4) 3k mn 7k m n 21k m n 2 3 2 3 5 5) 12 x y 2xy 24x y
9. 9. Power of Powers Simplify the following: ( x3 ) 4 The monomial is the term inside the parentheses.Step 1: Write out the expression in expanded form. 3 4 3 3 3 3 x x x x x x x x x x x x x x x x xStep 2: Simplify, writing as a power. 3 4 12 x x Note: 3 x 4 = 12.
10. 10. Power of Powers Rule n m mnFor any number, a, and all integers m and n, a a . 9 10 90 1) b b 3 3 9 2) c c 12 2 24 3) w w
11. 11. Monomials to PowersIf the monomial inside the parentheses has acoefficient, raise the coefficient to the power, butstill multiply the variable powers. 9 3 27 1) 2b 8b 3 3 9 2) 5c 125c 12 2 24 3) 7w 49w
12. 12. Monomials to Powers (Power of a Product)If the monomial inside the parentheses has morethan one variable, raise each variable to the outsidepower using the power of a power rule. (ab)m = am•bm 3 2 4 4 3 4 4 2 4 5w xy 5 w x y 34 4 24 625 w x y 12 4 8 625w x y
13. 13. Monomials to Powers (Power of a Product)Simplify each expression: 9 4 3 27 12 1) 2b c 8b c 5 3 3 15 9 2) 5a c 125a c 12 4 2 24 8 2 3) 7w y z 49w y z