I couldn't find a way to simplify to the same base. How do I do that?

I did: $2^{-1}-6^{(\sqrt{3}-1)(\sqrt{6}+3)}$

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  • $\begingroup$ are you trying to evaluate the expression? $\endgroup$ – Xiangyu Chen Feb 23 '18 at 0:14
  • $\begingroup$ @V.Chen no, I'm trying to simplify to a base to the power of something. $\endgroup$ – Nicolas Leskiu Feb 23 '18 at 0:15
  • $\begingroup$ @NicolasLeskiu Why would you want to simplify this to the same base? Isn't it fine in the form you left it? $\endgroup$ – Toby Mak Feb 23 '18 at 0:29

Suppose we have a number $6^a$, and want to convert it into the form $2^b$. Notice that: $$6^a = 2^{\log_2 6^a} = 2^{a \log_2 6},$$

so when we have $6^{(\sqrt{3}-1)(\sqrt6+3)}$, this becomes $2^{(\sqrt{3}-1)(\sqrt6+3) \log_2{6}}$.

Can you continue?

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