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Multiplying monomials

# Multiplying monomials - = 3 a 2 b 3 2 c 1 2 d = 3 a 2 b 5 c...

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Multiplying monomials Reminder: The rules and definitions for powers and exponents also apply in algebra.  Similarly,  a  ∙  a  ∙  a  ∙  b  ∙  b  =  a 3   b 2 To  multiply monomials,  add the exponents of the same bases.  Example 2 Multiply the following. 1. x 3 )(  x 4 ) =  x 3 + 4  =  x 7   2. x 2   y )(  x 3   y 2 ) = (  x 2   x 3 )(  yy 2 ) =  x 2 + 3   y 1 + 2  =  x 5   y 3   3. (6  k 5 )(5  k 2 ) = (6  ×  5)(  k 5   k 2 ) = 30  k 5 + 2  = 30  k 7   (multiply numbers)  4. –4(  m 2   n )(–3  m 4   n 3 ) = [(–4)(–3)](  m 2   m 4 )(  nn 3 ) = 12  m 2 + 4   n 1 + 3  = 12  m 6   n 4   (multiply  numbers)  5. c 2 )(  c 3 )(  c 4 ) =  c 2 + 3 + 4  =  c 9   6. (3  a 2   b 3   c )(  b 2   c 2   d ) = 3(  a 2 )(  b 3   b 2 )(  cc 2 )(  d ) = 3
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Unformatted text preview: ) = 3 a 2 b 3 + 2 c 1 + 2 d = 3 a 2 b 5 c 3 d Note that in example (d) the product of –4 and –3 is +12, the product of m 2 and m 4 is m 6 , and the product of n and n 3 is n 4 , because any monomial having no exponent indicated is assumed to have an exponent of l. When monomials are being raised to a power, the answer is obtained by multiplying the exponents of each part of the monomial by the power to which it is being raised....
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