Express the following fraction in simplest form, only using positive exponents. \[ \frac{10 h^{-6}}{\left(2 y^{-5} h\right)^{-1}} \]

To simplify the given expression \(\frac{10 h^{-6}}{\left(2 y^{-5} h\right)^{-1}}\), let's break it down step by step. First, simplify the denominator: \[ \left(2 y^{-5} h\right)^{-1} = \frac{1}{2 y^{-5} h} \] Applying the negative exponent gives us: \[ \left(2 y^{-5} h\right)^{-1} = \frac{1}{2} \cdot y^5 \cdot \frac{1}{h} = \frac{y^5}{2h} \] Now substitute this back into the original fraction: \[ \frac{10 h^{-6}}{\frac{y^5}{2h}} = 10 h^{-6} \cdot \frac{2h}{y^5} = \frac{20 h^{-5}}{y^5} \] Next, we want to express everything using positive exponents. Recall that \(h^{-5} = \frac{1}{h^5}\), hence we rewrite the fraction: \[ \frac{20}{y^5 h^5} \] Now everything is in simplest form: \[ \frac{20}{y^5 h^5} \] Thus, the final simplified expression is: \[ \frac{20}{y^5 h^5} \]