1. **State the problem:** Simplify the expression $$\sqrt[3]{8x} \cdot \sqrt[3]{8x^2}$$. 2. **Recall the property of cube roots:** For any real numbers $a$ and $b$, $$\sqrt[3]{a} \cdot \sqrt[3]{b} = \sqrt[3]{a \cdot b}$$. 3. **Apply the property:** $$\sqrt[3]{8x} \cdot \sqrt[3]{8x^2} = \sqrt[3]{(8x)(8x^2)}$$ 4. **Multiply inside the cube root:** $$(8x)(8x^2) = 64x^3$$ 5. **Simplify the cube root:** $$\sqrt[3]{64x^3} = \sqrt[3]{64} \cdot \sqrt[3]{x^3}$$ 6. **Evaluate each cube root:** $$\sqrt[3]{64} = 4$$ because $4^3 = 64$ $$\sqrt[3]{x^3} = x$$ (assuming $x \geq 0$ for real cube roots) 7. **Final answer:** $$4x$$ Thus, $$\sqrt[3]{8x} \cdot \sqrt[3]{8x^2} = 4x$$.