1. **State the problem:** Simplify the expression $$\sqrt[3]{\frac{49}{27}} \cdot j^{\frac{1}{3}}$$. 2. **Recall the property of radicals and exponents:** For any positive numbers $a$, $b$, and $c$, $$\sqrt[3]{\frac{a}{b}} = \frac{\sqrt[3]{a}}{\sqrt[3]{b}}$$ and $$x^{\frac{1}{3}} = \sqrt[3]{x}$$. 3. **Apply the property to the given expression:** $$\sqrt[3]{\frac{49}{27}} \cdot j^{\frac{1}{3}} = \frac{\sqrt[3]{49}}{\sqrt[3]{27}} \cdot \sqrt[3]{j}$$ 4. **Combine the cube roots:** $$= \frac{\sqrt[3]{49} \cdot \sqrt[3]{j}}{\sqrt[3]{27}} = \frac{\sqrt[3]{49j}}{\sqrt[3]{27}}$$ 5. **Simplify the denominator:** Since $$27 = 3^3$$, we have $$\sqrt[3]{27} = 3$$. 6. **Final simplified form:** $$\frac{\sqrt[3]{49j}}{3}$$ **Answer:** $$\frac{\sqrt[3]{49j}}{3}$$