In the big O notation with multiple variables ($n,m$), is $O((n+1)^m) = O(n^m)$?
Details:
My intuition said yes, since adding a constant should neither have an effect in big O notation, even in a base. But since the exponent is also a variable and not a constant, I am not able to prove it. I tried for several definitions for Big O with multiple variables (such as the one on the wikipedia page and the one on this math.SE precious question), but did not find suitable estimates.