How do you simplify #(3r^7)/(2r^2)^4#?

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Answer 1 · 2016-10-29T05:12:58

#3/(16r)#

This fraction is simplified by using the power identities of powers with same base

#color(blue)((r^n)^m=r^(nxxm)#

#color(red)(r^m/r^n=r^(m-n))#

#color(purple)((axxb))^m=a^mxxb^m#

#(3r^7)/(2r^2)^4=(3r^7)/(2^4color(blue)(r^(2xx4)))#

#(3r^7)/(2r^2)^4=(3r^7)/(2^4r^8)#

#(3r^7)/(2r^2)^4=(3/2^4)(r^7/r^8)#

#(3r^7)/(2r^2)^4=(3/16)color(red)(r^(7-8))#

#(3r^7)/(2r^2)^4=(3r^(-1))/16#

#(3r^7)/(2r^2)^4=3/(16r)#