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Monomials Dividing and Reducing Monomials The Zero Power Rule Zero Property of Exponents A nonzero number to the zero power is 1: a 1, a 0 0 1) 7 1 0 2) 4a 1 0 3) 2a b w 1 7 4 0 Quotient of Powers 7 Simplify the following expression: a 5 a •Step 1: Write out the expressions in expanded form. a a a a a a a a 5 a a a a a a 7 •Step 2: Cancel matching factors (A factor is a term that is multiplied by the rest of the expression; here, ‘a’ is a factor.). a a a a a a a a a 2 2 a 5 a a a a a a 1 7 Quotient of Powers Rule Let’s look at the results: a7 a2 2 a 5 a 1 Notice: • the base is still ‘a’. • the power is 2 = (7 - 5). • the term that didn’t cancel is in the numerator (where the larger power was to begin with). For all values, a, and all integers m and n: am m n a , a 0. n a Quotient of Powers Rule 1) 2) 3) 4) a5 7 a 5 w 2 w 5 6 7 6 52 2 5 1 2 a 3 w 3 w 1 1 1 2 6 36 5 1 0 Dividing Monomials These monomials have coefficients and more than one variable. Reduce the coefficients as you would with a typical fraction and use the power rule for the variables. x 3y 8 x5 y9 3 8 xy 1) 2 1 xy 3 15x 4 2) 2 6 5x 25x 36a 5 b3 9a 3 3) 6 2 9 5b 20a b Power of a Quotient 3 3 Simplify the following: 2 Step 1: Distribute the power to both the numerator & denominator. 3 3 3 3 2 23 Step 2: Find the powers of the numerator & denominator. 3 3 27 2 8 Step 3: Reduce if you can. Power of a Quotient Rule m a am For any numbers, a & b, and all integers m, b bm . 10 a a 1) 2 20 b b 3 3 1 1 1 2) 3 5 5 125 2 3x 2 9x 2 3x 3) 2 2 4 2 7y 7y 49y 3 30