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

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

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

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

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

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

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

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

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

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

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