Question 197349
*[Tex \LARGE \log_{6}\left(216^{-3}\right)] ... Start with the given expression.



*[Tex \LARGE \log_{6}\left(\left(6^3\right)^{-3}\right)] ... Rewrite 216 as {{{6^3}}}



*[Tex \LARGE \log_{6}\left(6^{-3\ast3}\right)] ... Multiply the exponents.



*[Tex \LARGE \log_{6}\left(6^{-9}\right)] ... Multiply



*[Tex \LARGE -9\log_{6}\left(6\right)] ... Pull down the exponent.



*[Tex \LARGE -9(1)] ... Evaluate the log base 6 of 6 to get 1



*[Tex \LARGE -9] ... Multiply



So *[Tex \LARGE \log_{6}\left(216^{-3}\right) = -9]