How do you simplify #\frac { 2^ { 3} r ^ { 4} ( r ^ { - 3} ) ^ { - 1} } { 2^ { 6} r ^ { - 3} }#?

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Answer 1 · 2016-11-14T16:45:13

#(r^10)/(8)#

#(2^3r^4(r^-3)^-1)/(2^6r^-3)-># distribute the negative one exponent

#=(2^3r^4(r^(-3(-1))))/(2^6r^-3)=(2^3r^4(r^3))/(2^6r^-3)#

#2^3=2*2*2#
#2^6=2*2*2*2*2*2#

So

#=((2^3)r^4r^3)/((2^6)r^-3)=((cancel2*cancel2*cancel2)r^4r^3)/((cancel2*cancel2*cancel2*2*2*2)r^-3)= (r^4r^3)/(2^3r^-3)#

Bring #r^-3# up the sign of the exponent will revert (change to positive)

#=(r^4r^3r^3)/2^3-># add the exponents

#=(r^(4+3+3))/2^3=r^10/2^3=r^10/8#