How do you simplify #((2•2^3) / 2) ^2#?

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Answer 1 · 2016-07-11T19:07:40

Assuming you mean #((2xx2^3)/2)^2#

64

I have deliberately done it this way to demonstrate some actions

#2xx2^3 = 2^(3+1) =2^4# giving

#((2^4)/2)^2#

But #2^4/2# is the same as #2^(4-1)=(cancel(2)xx2xx2xx2)/(cancel(2)) =2^3# giving:

#(2^3)^2#

But this is the same as #2^3xx2^3" " =" " 2^(3+3)" "=" "2^(3xx2) = 64#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Using shortcuts")#

#((cancel(2)xx2^3)/(cancel(2)))^2 = 2^6=64#