1. **State the problem:** We need to find the value of $$9^{\frac{1}{2}} \div 5^{-2}$$ and express the answer as a whole number or a simplified fraction. 2. **Recall the rules and formulas:** - The expression $$a^{\frac{1}{2}}$$ means the square root of $$a$$. - Negative exponents mean reciprocal: $$a^{-n} = \frac{1}{a^n}$$. - Division of powers can be rewritten as multiplication by the reciprocal. 3. **Evaluate each part:** - $$9^{\frac{1}{2}} = \sqrt{9} = 3$$. - $$5^{-2} = \frac{1}{5^2} = \frac{1}{25}$$. 4. **Rewrite the division as multiplication:** $$9^{\frac{1}{2}} \div 5^{-2} = 3 \div \frac{1}{25} = 3 \times 25$$. 5. **Calculate the product:** $$3 \times 25 = 75$$. 6. **Final answer:** $$\boxed{75}$$