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For a separable metric space X, we consider possibilities for the sequence $S\left(X\right)=d_n:n\in \mathbb{N}$ where $d_n=dim{X}^n$. In Section 1, a general method for producing examples is given which can be used to realize many of the possible sequences. For example, there is $X_n$ such that $S\left(X_n\right)=n,n+1,n+2,...$, $Y_n$, for n >1, such that $S\left(Y_n\right)=n,n+1,n+2,n+2,n+2,...$, and Z such that S(Z) = 4, 4, 6, 6, 7, 8, 9,.... In Section 2, a subset X of ${ℝ}^2$ is shown to exist which satisfies $1=dimX=dim{X}^2$ and $dim{X}^3=2$.