Simplify. Express your answer with positive exponents. Assume that all variables are nonzero. \( \frac{7 x^{-4} y^{-5}}{4 z^{-3}} \)

To simplify the expression \( \frac{7 x^{-4} y^{-5}}{4 z^{-3}} \), we start by separating the constants from the variables. This gives us: \[ \frac{7}{4} \cdot \frac{x^{-4}}{1} \cdot \frac{y^{-5}}{1} \cdot z^3 \] Now, we can rewrite the expression using positive exponents. Recall that \(a^{-n} = \frac{1}{a^n}\). Therefore, we can rewrite \(x^{-4}\) and \(y^{-5}\) as: \[ \frac{7}{4} \cdot \frac{z^3}{x^4 y^5} \] Finally, combining everything, we get: \[ \frac{7 z^3}{4 x^4 y^5} \] So, the simplified expression is \( \frac{7 z^3}{4 x^4 y^5} \).