√6 simply means [tex] 6^{1/2} [/tex]
When you have a power to the power, you multiply the exponents, so it's
[tex] \frac{6 ^{1/2*4} }{ 6^{1/2*5} } = \frac{6^{2} }{6 ^{5/2} } [/tex]
Then when you divide numbers with the same base with exponents, you subtract the exponents, so it is [tex] 6^{2-(5/2)} =6 x^{123} = 6 ^{-1/2} = \frac{1}{ \sqrt{6} } [/tex]
