1. **State the problem:** We need to evaluate the expression $\left(3(5)-4(-2)\right)^2$. 2. **Apply the order of operations:** First, calculate the products inside the parentheses. 3. Calculate $3(5)$: $$3 \times 5 = 15$$ 4. Calculate $-4(-2)$: $$-4 \times -2 = 8$$ 5. Substitute these values back into the expression: $$\left(15 + 8\right)^2$$ 6. Simplify inside the parentheses: $$15 + 8 = 23$$ 7. Now square the result: $$23^2 = 529$$ **Final answer:** $529$