Given expression: [tex]\frac{((6^{-4})^{-9})}{6^6}[/tex].
First we would apply exponents of exponent rule on the top.
[tex](a^m)^n= a^{m\times n}[/tex]
Therefore,
[tex]((6^{-4})^{-9}) = (6)^{-4\times -9} = (6)^{36}[/tex]
=[tex]\frac{((6^{-4})^{-9})}{6^6} = \frac{6^36}{6^6}[/tex]
Applying quotient rule of exponents.
[tex]\frac{a^m}{a^n} = a^{m-n}[/tex]
[tex]Therefore \ \frac{6^{36}}{6^6} =6^{36-6}[/tex]
= [tex]6^{30}[/tex]
