1. **State the problem:** Simplify the expression $$\frac{r^5 g^2 h}{10 h \cdot r^0 g^4 h^{-3}}$$. 2. **Recall the rules:** - Any number or variable raised to the power 0 is 1, so $r^0 = 1$. - When dividing powers with the same base, subtract the exponents: $$\frac{a^m}{a^n} = a^{m-n}$$. - When dividing, constants remain as is unless simplified. 3. **Rewrite the expression:** $$\frac{r^5 g^2 h^1}{10 \cdot 1 \cdot g^4 h^{-3}} = \frac{r^5 g^2 h^1}{10 g^4 h^{-3}}$$ 4. **Apply the division of powers:** - For $r$: $$r^{5-0} = r^5$$ - For $g$: $$g^{2-4} = g^{-2}$$ - For $h$: $$h^{1 - (-3)} = h^{1+3} = h^4$$ 5. **Rewrite the expression with simplified exponents:** $$\frac{r^5 g^{-2} h^4}{10}$$ 6. **Express negative exponent as reciprocal:** $$g^{-2} = \frac{1}{g^2}$$ 7. **Final simplified expression:** $$\frac{r^5 h^4}{10 g^2}$$ **Answer:** $$\boxed{\frac{r^5 h^4}{10 g^2}}$$