# Growth in direct product

I started reading with growth of groups. The problem is the following:

Problem : Let $G$ be an infinite finitely generated group. a. If $G$ is polynomial growth then so is $G^m$ (a direct product of $G$). Moreover, the growth function $\gamma_G$ is not equivalent of $\gamma_{G^m}$ unless $m=1$. b. If $G$ is exponential growth then so is $G^m$, and their growth functions are equivalent.

Could any one give me a hint. Thanks in advance.

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Maybe try showing that $\gamma_{G^m}=\gamma_G^m$. – Steve D Nov 20 '12 at 10:14