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May 8, 2019 at 23:32 comment added John L. The single exponentiation $c^d$ seems like red erring in most situations because of, for example, the reason you have specified $10^{10000000}+1$. If you meant the unique factorization of integers or rationals, there might be more than a few prime factors such as $2\times3^2\times5^{-3}\times7^3\times11^{-5}$. (This comment also supports your view that "there is no one answer that will handle everything efficiently.")
May 8, 2019 at 23:18 history answered D.W. CC BY-SA 4.0