# Proving that the sum of DTIME and DSPACE are not equal

I have an example question from a textbook where it asks to prove that $\Sigma_k DTIME(2^{n^k}) \neq DSPACE(2^n)$.

There isn't a solution provided in the textbook. I've been working with a solution involving padding but I haven't been able to come up with a solution.

Any tips would be appreciated! Thanks in advance.

• Try mimicking the proof of your favorite hierarchy theorem. – Yuval Filmus Mar 31 '18 at 17:44