Solve (1/216)^(-4): Negative Exponent with Product Fraction

To solve this problem, we'll follow these steps:

• Step 1: Identify the negative exponent and use the rule $\left(\frac{a}{b}\right)^{-n} = \left(\frac{b}{a}\right)^n$.
• Step 2: Apply the rule to the expression $\left(\frac{1}{4 \times 6 \times 9}\right)^{-4}$.
• Step 3: Simplify the result.

Now, let's work through each step:
Step 1: The given expression is $\left(\frac{1}{4 \times 6 \times 9}\right)^{-4}$. Notice the negative exponent $-4$.
Step 2: According to the rule, flipping the fraction and changing the sign of the exponent, we get $\left(4 \times 6 \times 9\right)^{4}$.
Step 3: Thus, the expression simplifies to $4^4 \times 6^4 \times 9^4$.

Therefore, the solution to the problem is $4^4 \times 6^4 \times 9^4$, which corresponds to choice 2.