1. **State the problem:** Simplify the expression $$\frac{10a^2}{15a^6}$$. 2. **Write down the formula and rules:** When simplifying fractions with variables, divide the coefficients and subtract the exponents of like bases using the rule $$\frac{a^m}{a^n} = a^{m-n}$$. 3. **Simplify the coefficients:** $$\frac{10}{15} = \frac{\cancel{5} \times 2}{\cancel{5} \times 3} = \frac{2}{3}$$. 4. **Simplify the variables:** $$\frac{a^2}{a^6} = a^{2-6} = a^{-4}$$. 5. **Combine the simplified parts:** $$\frac{10a^2}{15a^6} = \frac{2}{3} a^{-4}$$. 6. **Rewrite with positive exponents:** $$a^{-4} = \frac{1}{a^4}$$, so the expression becomes $$\frac{2}{3a^4}$$. **Final answer:** $$\boxed{\frac{2}{3a^4}}$$