1. **State the problem:** Simplify the expression $$e^{2x+3} \left(e^{3x-5}\right)^2$$. 2. **Recall the exponent rules:** When multiplying expressions with the same base, add the exponents: $$a^m \cdot a^n = a^{m+n}$$. 3. **Apply the power rule:** For an exponent raised to another power, multiply the exponents: $$\left(a^m\right)^n = a^{mn}$$. 4. **Simplify the given expression:** $$e^{2x+3} \left(e^{3x-5}\right)^2 = e^{2x+3} \cdot e^{2(3x-5)} = e^{2x+3} \cdot e^{6x-10}$$ 5. **Add the exponents:** $$2x + 3 + 6x - 10 = 8x - 7$$ 6. **Final simplified form:** $$e^{8x - 7}$$ **Answer:** a. $$e^{8x-7}$$