What is the value of n in the equation 2^2x2^n =(2^4)^3

Please use * to indicate mult., not "x."

Then 2^2*2^n = (2^4)^3
           4*2^n =   16^3
2 is the base of the first exponential, and 16 is the base of the second.

Rewrite 16 as 2^4 (as it was originally given).

Then     4*2^n = (2^4)^3

This is equivalent to 2^(n+2) = 2^12
Solving for n:  n+2 = 12, and so n = 10 (answer.  You should check this.