Answer
$\frac{n^{24}}{81}$
Work Step by Step
We start with the given expression: $(3n^{-6})^{-4}$
To raise a product to a power, we raise each factor to the power and multiply: $3^{-4}(n^{-6})^{-4}$
To raise a power to a power, we multiply the exponents: $3^{-4}n^{24}$
The negative exponent rule states that for every nonzero number $a$ and integer $n$, $a^{-n}=\frac{1}{a^n}$. We use this rule to rewrite the expression: $\frac{n^{24}}{3^{4}}$
We expand the exponent in the denominator: $\frac{n^{24}}{3\times3\times3\times3}=\frac{n^{24}}{81}$
