0
$\begingroup$

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

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

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

| cite | improve this question | | | | |
$\endgroup$
  • $\begingroup$ 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
0
$\begingroup$

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?

| cite | improve this answer | | | | |
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.