# Simplify to the same base

$(2^{0.5})^{-2}-(\frac{6^{\sqrt{3}}}{6})^{\sqrt{6}+3}$

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

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

• are you trying to evaluate the expression? – Xiangyu Chen Feb 23 '18 at 0:14
• @V.Chen no, I'm trying to simplify to a base to the power of something. – Nicolas Leskiu Feb 23 '18 at 0:15
• @NicolasLeskiu Why would you want to simplify this to the same base? Isn't it fine in the form you left it? – 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 $2^{(\sqrt{3}-1)(\sqrt6+3) \log_2{6}}$.