15 01 Multiplying Monomials A monomial is a

15. 01 Multiplying Monomials

A monomial is a number, a variable, or a product of both. Examples: 8 , x , 5 y , x 3 , 4 x 2 , – 6 xy 7 Exponential Notation m a a is called the base. m is called the exponent or power. The exponent indicates how many times to multiply the base by itself

m a means |________| a · a ···· a x 3 = x · x 9 x 2 y 2 = 9 · x · y m times 8 y 4 = 8 · y · y (5 w) 2 = 5 w · 5 w Write w · w · w using exponents. = w 5 Write 2 · y · y · 3 using exponents. = 6 y 3 Write x · y · x using exponents. = x 3 y 2 Write 4 x · 4 x using exponents. = (4 x) 3 or 64 x 3

Simplify x 3 · x 2 = x·x·x = x 5 2 w 4 · 8 w 2 = 2·w·w · 8·w·w = 16 w 6 We want to find a rule that eliminates all these steps. When multiplying monomials, add the exponents of the variables that have the same base. m a · n a = m + n a If there are coefficients, multiply the coefficients first.

am · an = am+n Simplify the following expressions. x 5 · x 3 = x 5+3 = x 8 y 7 · y – 3 = y 7 + (– 3) x 4 y 6 · xy 8 = x 4+1 = y 4 y 6+8 3 x 5 · 5 x 9 = (3 · 5)(x 5 · x 9) – 6 x 5 y · 9 xy 3 = = x 5 y 14 Important x = x 1 = 15 x 14 (– 6 · 9)(x 5 · x)(y · y 3) = – 54 x 6 y 4

m a Try This: · n a = m + n a Simplify the following expressions x 9 · x = x 10 x 3 y 5 · x– 3 y 8 = 2 x 4 · 8 x 7 = y 8 · y– 2 = y 6 x 0 y 13 16 x 11 – 8 xy · 7 xy 2 = – 56 x 2 y 3 x 6 y 2 · 3 xy 4 = 3 x 7 y 6 Important x = x 1