Simplify. \[ \left(2 x^{5} y^{-4}\right)^{3} \] Write your answer using only positive exponents. \( \square \)

To simplify \(\left(2 x^{5} y^{-4}\right)^{3}\), we can apply the power of a product rule, which states that \((a \cdot b)^n = a^n \cdot b^n\). So, we have: \[ \left(2\right)^{3} \cdot \left(x^{5}\right)^{3} \cdot \left(y^{-4}\right)^{3} = 8 \cdot x^{15} \cdot y^{-12} \] Next, to express the answer with only positive exponents, we rewrite \(y^{-12}\) as \(\frac{1}{y^{12}}\). Thus, we get: \[ \frac{8x^{15}}{y^{12}} \] So, the final simplified expression is: \[ \frac{8x^{15}}{y^{12}} \]