How do you multiply #(27r^5)/(7s)*(28rs^3)/(9r^3s^2)#?

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Answer 1 · 2018-03-03T01:49:54

The simplified answer is #12r^3#.

First, simplify given expression:

#color(white)=(27r^5)/(7s)*(28rs^3)/(9r^3s^2)#

#=(27r^5)/(7s)*(28color(red)cancel(color(black)r)s^3)/(9 r^stackrel2color(red)cancel(color(black)3)s^2)#

#=(27r^5)/(7s)*(28s^color(red)cancel(color(black)3))/(9r^2color(red)cancel(color(black)(s^2))#

#=(27r^5)/(7s)*(28s)/(9r^2)#

Next, multiply the numerators and denominators:

#color(white)=(27r^5)/(7s)*(28s)/(9r^2)#

#=(27r^5*28s)/(7s*9r^2)#

#=(756r^5s)/(63r^2s)#

#=(stackrel12 color(red)cancel(color(black)756)r^5s)/(color(red)cancel(color(black)63)r^2s)#

#=(12r^(stackrel3 color(red)cancel(color(black)5))s)/(color(red)cancel(color(black)(r^2))s)#

#=(12r^3color(red)cancel(color(black)s))/color(red)cancel(color(black)s)#

#=12r^3#

This is as simplified as it gets.