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

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Answer 1 · 2016-07-04T06:47:25

#(2^3*(2^2)^3)^2/2=2^17#

We can use here three formulas relating to exponents;

#a^m*a^n=a^((m+n))#, #a^m/a^n=a^((m-n))# and #(a^m)^n=a^((mxxn))#

Hence #(2^3*(2^2)^3)^2/2#

= #(2^3*2^((2xx3)))^2/2#

= #(2^3*2^6)^2/2#

= #(2^((3+6)))^2/2#

= #(2^9)^2/2^1# (as #a=a^1#)

= #2^((9xx2))/2^1#

= #2^18/2^1#

= #2^((18-1))#

= #2^17#