How do you simplify #[(4^2)^3]^2#?

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Answer 1 · 2017-05-20T10:33:26

#4^12#

According to the 4th index law

#(a^x)^y#

#a^(x xx y)#

#(4^2)^3)^2#

#(4^(2xx3))^2#

#(4^6)^2#

#4^(6xx2)#

#4^12#

Answer 2 · 2017-05-20T10:38:26

#4^12#

For reference, the index law used here is
#(a^x)^y=a^(xy)#

So. You just apply that index law step by step until there are no more brackets.
#[(4^2)^3]^2#
#=(4^2)^(3xx2)#
#=(4^2)^6#
#=4^(2xx6)#
#=4^12#

That's the simplified answer, which is what you asked for, but if you wanted the answer without any indices;
#4^12=16,777,216#

Hope that helps! :)