fozzzy wrote:

Given \(2^{4x} = 1600\), what is the value of \(\frac{[2^{(x-1)}]^4}{[2^x]^2}\)

A. 2

B. 5/2

C. 5

D. 25/4

E. 24

I need to improve my speed on these questions... Took me 5 minutes because I made careless mistakes and had to re-do the question 3 times.

My reasoning:

We can simply both equations to get the values we need.

\(\frac{[2^{(x-1)}]^4}{[2^x]^2} = \frac{[2^{(4x-4)}]}{[2^x]^2} = \frac{[2^{4x}] +[2^{-4}]}{[2^2x]}\)

From \(2^{4x} = 1600\) we can square both sides by \(\frac{1}{2}\) to get \(2^{2x} = 40\)

Plugging everything back into the question we get

\(\frac{1600}{40*16}\) = \(\frac{5}{2}\)