1. **State the problem:** Simplify the expression $$\frac{f^5 g^2 h}{f^0 g^4 h^{-1}}$$. 2. **Recall the rules:** - Any number to the zero power is 1, so $f^0 = 1$. - When dividing powers with the same base, subtract the exponents: $$\frac{a^m}{a^n} = a^{m-n}$$. - Negative exponents mean reciprocal: $$a^{-n} = \frac{1}{a^n}$$. 3. **Apply the rules:** $$\frac{f^5 g^2 h}{f^0 g^4 h^{-1}} = f^{5-0} g^{2-4} h^{1-(-1)}$$ 4. **Simplify exponents:** $$= f^5 g^{-2} h^{2}$$ 5. **Rewrite negative exponent:** $$= f^5 \frac{h^2}{g^2}$$ 6. **Final simplified expression:** $$\boxed{\frac{f^5 h^2}{g^2}}$$