Answer:
6³⁰
Step-by-step explanation:
To simplify the given expression [tex]\dfrac{(6^{-4})^{-9}}{6^6}[/tex], we can use the rule of indices (exponents).
The rule we will use Power rule:
[tex] \Large\boxed{\boxed{ (a^m)^n = a^{mn}}} [/tex]
Now, let's apply this rule to the numerator:
[tex] (6^{-4})^{-9} = 6^{(-4)(-9)} = 6^{36} [/tex]
Now, substitute this into the original expression:
[tex] \dfrac{6^{36}}{6^6} [/tex]
Now, use another rule of indices (Quotient of Powers rules) which states that when we divide powers with the same base, we subtract the exponents :
[tex]\Large\boxed{\boxed{ a^m \div a^n = a^{m-n}}} [/tex]
Applying this to the expression:
[tex] 6^{36-6} = 6^{30} [/tex]
So, the simplified form of the expression is:
[tex]\Large\boxed{\boxed{6^{30}}}[/tex]
