1. **State the problem:** Simplify the expression $\frac{a^2}{a^{-3}}$. 2. **Recall the rule for division of exponents with the same base:** When dividing powers with the same base, subtract the exponents: $$\frac{a^m}{a^n} = a^{m-n}$$ 3. **Apply the rule:** $$\frac{a^2}{a^{-3}} = a^{2 - (-3)}$$ 4. **Simplify the exponent:** $$2 - (-3) = 2 + 3 = 5$$ 5. **Final simplified expression:** $$a^5$$ So, $\frac{a^2}{a^{-3}} = a^5$.