Evaluate (5/594)^(-3): Negative Exponent Expression Solution

To solve this problem, we will employ exponent rules:

• Convert the negative exponent: $\left(\frac{5}{6 \times 9 \times 11}\right)^{-3} = \left(\frac{6 \times 9 \times 11}{5}\right)^3$.
• Simplify using the power of a quotient: $\left(\frac{6 \times 9 \times 11}{5}\right)^3 = \frac{(6 \times 9 \times 11)^3}{5^3}$.
• Further expand separately: $\frac{6^3 \times 9^3 \times 11^3}{5^3}$.

Therefore, each proposed expression $\frac{6^3 \times 9^3 \times 11^3}{5^3}$, $\frac{(6 \times 9 \times 11)^3}{5^3}$, and $\left(\frac{6 \times 9 \times 11}{5}\right)^3$ are equivalent and correct interpretations of the original expression.

All answers are correct.

The correct choice is option 4: All answers are correct.