# May I get a comment on this proof?

flyingpig

## Homework Statement

Prove directly:

Prove that if $$2^{2x}$$ is odd integer, then $$4^{x}$$ is odd integer

## The Attempt at a Solution

$$2^{2x} = 2k + 1$$ for some k is integer

$$2^{2x} = 4^{x} = 2k + 1$$

Thus completes the proof?

Am I allow to make the assumption (fact) $$2^{2x} = 4^{x}$$?

Thanks

That is correct. It is indeed true that $a^{bc}=(a^b)^c$.