1. **State the problem:** Evaluate the expression $$\sqrt[3]{3k} + 5k$$ when $$k = -72$$. 2. **Recall the formula and rules:** The cube root of a number $$a$$ is a value $$b$$ such that $$b^3 = a$$. Also, substitution means replacing $$k$$ with $$-72$$ in the expression. 3. **Substitute $$k = -72$$ into the expression:** $$\sqrt[3]{3(-72)} + 5(-72)$$ 4. **Simplify inside the cube root:** $$3 \times (-72) = -216$$ So the expression becomes: $$\sqrt[3]{-216} + (-360)$$ 5. **Evaluate the cube root:** Since $$(-6)^3 = -216$$, we have: $$\sqrt[3]{-216} = -6$$ 6. **Calculate the entire expression:** $$-6 + (-360) = -6 - 360 = -366$$ **Final answer:** $$-366$$