How to calculate exponent (2^2x)(4^x)(8^-x)?

We need to convert each term to the same base, in this
case, 2.

The first term already has a base of 2.  The
second term has a base of 4, which is 2^2, and the third term has a base of 8, which is
the same as 2^3.  So we
have:

[2^(2x)][4^x][8^(-x)]

=
[2^(2x)][(2^2)^x][(2^3)^(-x)]

When you have powers of
powers, you multiply the exponents, so we can rewrite it
as:

=
[2^2x][2^2x][(2^(-3x)]

And since we now have the same base,
we can add the exponents.

=
2^(2x+2x-3x)

=
2^x

The exponent on the final answer is
x.