Help with pre-algebra - simplifying

Would the expression (2^4*(2^-4)^2)^3/(2^0) simplify to 4,096?

That's not the answer that I get.

Work the numerator from the inside out:

2^(-4) = 1/2^(4) = 1/16

(1/16)^2 = 1/256


2^4 = 16

Multiply those:

(1/256) * 16 = 1/16

Cube that:

(1/16)^3 = 1/4096


For the denominator, raising any number to the zero power is 1:

2^0 = 1

Since 1/4096 is being divided by 1, the 1/4096 is the simplification.

[added]
Note: 1/4096 = 2^(-12)

(2^4*(2^-4)^2)^3/(2^0)

First (2^-4)^2 = 2^-4*2 = 2^-8

(2^4*2^-8)^3/(2^0)

Second 2^4*2^-8) = 2^4-8 = 2^-4

(2^-4)^3 / 2^0

Third (2^-4)^3 = 2^-12
And 2^0 = 1

2^-12 / 1 = 2^-12