How do you multiply #(3m ^ { 5} n ^ { 4} ) ( 7m ^ { 9} n )#?

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Answer 1 · 2017-03-29T18:46:46

See the entire solution process below:

First, rewrite this express as:

#(3 xx 7)(m^5m^9)(n^4n) -> 21(m^5m^9)(n^4n)#

Now, use these two rules for exponents to complete the multiplication:

#a = a^color(blue)(1)# and #x^color(red)(a) xx x^color(blue)(b) = x^(color(red)(a) + color(blue)(b))#

#21(m^5m^9)(n^4n) -> 21(m^color(red)(5) xx m^color(blue)(9))(n^color(red)(4) xx n^color(blue)(1)) =#

#21m^(color(red)(5) + color(blue)(9))n^(color(red)(4) + color(blue)(1)) =#

#21m^14n^5#