I'm trying to solve this operation for a computer algorithms course practice set. I originally assumed that $\log_2(n)^{\log_2(n^5)} = \log_2(n^5) = 5\log_2(n)$ But I know that's not correct.
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Just looking at the graph it doesn’t look like it really simplifies well. Edit: wolfram alpha agrees with me – Snacc Feb 12 '20 at 02:05
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You can alternatively write it as $n^{5log_{2}(log{2}(n))}$ if that helps – Dolma Mar 26 '20 at 00:58