1. **State the problem:** Simplify the expression $$\frac{g^7 h^9}{5 g^2 h^7}$$ and express the answer using exponents. 2. **Recall the exponent rules:** When dividing like bases, subtract the exponents: $$\frac{a^m}{a^n} = a^{m-n}$$. 3. **Apply the rule to each base:** $$\frac{g^7}{g^2} = g^{7-2} = g^5$$ $$\frac{h^9}{h^7} = h^{9-7} = h^2$$ 4. **Rewrite the expression with simplified exponents:** $$\frac{g^7 h^9}{5 g^2 h^7} = \frac{\cancel{g^7} h^9}{5 \cancel{g^2} h^7} = \frac{g^{7-2} h^{9-7}}{5} = \frac{g^5 h^2}{5}$$ 5. **Final simplified expression:** $$\frac{g^5 h^2}{5}$$ This is the simplified form with exponents.