Express the following fraction in simplest form, only using positive expol \[ \frac{3\left(h^{-5}\right)^{4}}{6 h^{6}} \]

To simplify the given fraction \(\frac{3\left(h^{-5}\right)^{4}}{6 h^{6}}\), we start by simplifying the numerator. First, we calculate \(\left(h^{-5}\right)^{4}\): \[ \left(h^{-5}\right)^{4} = h^{-20} \] Now substituting this back into the expression, we have: \[ \frac{3 h^{-20}}{6 h^{6}} \] Next, we can simplify the coefficients: \[ \frac{3}{6} = \frac{1}{2} \] This gives us: \[ \frac{1}{2} \cdot \frac{h^{-20}}{h^{6}} \] Using the rule of exponents \(\frac{h^a}{h^b} = h^{a-b}\), we combine the terms: \[ h^{-20 - 6} = h^{-26} \] So the expression now looks like: \[ \frac{1}{2} h^{-26} \] To express this in positive exponents, we can rewrite \(h^{-26}\) as \(\frac{1}{h^{26}}\): \[ \frac{1}{2 h^{26}} \] Thus, the simplest form of the given fraction is: \[ \frac{1}{2 h^{26}} \]