Question

(\frac{-3h^{3}}{(3h^{-5})^{2}})

Explanation:

Step1: Simplify the denominator using power of a product and power of a power rules.

The denominator is \((3h^{-5})^2\). By the power of a product rule \((ab)^n = a^n b^n\) and power of a power rule \((a^m)^n=a^{mn}\), we have:
\((3h^{-5})^2 = 3^2\times(h^{-5})^2 = 9h^{-10}\)
So the expression becomes \(\frac{-3h^3}{9h^{-10}}\)

Step2: Simplify the coefficient and the variable part separately.

For the coefficient: \(\frac{-3}{9}=-\frac{1}{3}\)
For the variable part, use the rule \(\frac{a^m}{a^n}=a^{m - n}\). Here \(m = 3\) and \(n=- 10\), so \(h^{3-(-10)}=h^{13}\)

Step3: Combine the coefficient and the variable part.

Multiply the simplified coefficient and the simplified variable part: \(-\frac{1}{3}\times h^{13}=-\frac{h^{13}}{3}\)

Answer:

\(-\frac{h^{13}}{3}\)