# Is NSPACE(2^O(n)) = NSPACE(n^2 * 2^(O(n))

As said in the title, i am quite curious wether NSPACE(2^(O(n)) equals NSPACE(n^2 * 2^(O(n))

I am aware of the fact, that NSPACE(k * 2^O(n)) equals NSPACE(2^O(n)) due to linear space reduction (i.e. some sort of super character representing k characters)

But since neighter n nor n^2 is linear, we cant use this here.

Yes. Clearly NSPACE($$2^{O(n)}$$) $$\subseteq$$ NSPACE($$n^2 \cdot 2^{O(n)}$$).
To show that NSPACE($$2^{O(n)}$$) $$\supseteq$$ NSPACE($$n^2 \cdot 2^{O(n)}$$) it suffices to notice that $$n^2 \cdot 2^{O(n)} = 2^{O(n) + 2\log n}$$ and $$O(n)+2\log n =O(n)$$.