1. **Problem 2:** Simplify the expression $$\frac{\sqrt[3]{3m^{2}n^{4}}}{\sqrt[3]{4m^{4}n^{4}}}$$. 2. Use the property of cube roots: $$\frac{\sqrt[3]{a}}{\sqrt[3]{b}} = \sqrt[3]{\frac{a}{b}}$$. 3. Apply this to get: $$\sqrt[3]{\frac{3m^{2}n^{4}}{4m^{4}n^{4}}}$$ 4. Simplify inside the cube root: $$\frac{3}{4} \cdot \frac{m^{2}}{m^{4}} \cdot \frac{n^{4}}{n^{4}} = \frac{3}{4} \cdot m^{2-4} \cdot n^{4-4} = \frac{3}{4} m^{-2} n^{0}$$ 5. Since $$n^{0} = 1$$, the expression becomes: $$\sqrt[3]{\frac{3}{4} m^{-2}}$$ 6. Rewrite $$m^{-2}$$ as $$\frac{1}{m^{2}}$$: $$\sqrt[3]{\frac{3}{4} \cdot \frac{1}{m^{2}}} = \sqrt[3]{\frac{3}{4m^{2}}}$$ 7. Final simplified form: $$\boxed{\sqrt[3]{\frac{3}{4m^{2}}}}$$ --- 1. **Problem 3:** Given $$g(x) = -3 + (x - 1)^{3}$$ and $$y = -1 + \sqrt[3]{x + 3}$$, describe and plot the graphs. 2. The function $$g(x) = -3 + (x - 1)^{3}$$ is a cubic function shifted right by 1 and down by 3. 3. The function $$y = -1 + \sqrt[3]{x + 3}$$ is a cube root function shifted left by 3 and down by 1. 4. Both functions have characteristic cubic shapes: S-shaped curves with inflection points at their respective shifts. 5. The graph requested is for $$g(x)$$ on coordinate axes from -6 to 6. 6. The graph of $$g(x)$$ has an inflection point at $$x=1, y=-3$$. 7. The graph of $$y = -1 + \sqrt[3]{x + 3}$$ has an inflection point at $$x=-3, y=-1$$. Final answers: - Simplified expression for problem 2: $$\sqrt[3]{\frac{3}{4m^{2}}}$$ - Functions for problem 3: $$g(x) = -3 + (x - 1)^{3}$$ and $$y = -1 + \sqrt[3]{x + 3}$$