1. **State the problem:** Determine whether the two expressions $$\frac{3x^3}{2}$$ and $$\frac{6x^4}{4}$$ are equivalent. 2. **Recall the rule for equivalence:** Two expressions are equivalent if they simplify to the same expression for all values of $x$. 3. **Simplify each expression:** - First expression: $$\frac{3x^3}{2}$$ (already simplified). - Second expression: $$\frac{6x^4}{4} = \frac{\cancel{6} \times x^4}{\cancel{4}} = \frac{3x^4}{2}$$ after dividing numerator and denominator by 2. 4. **Compare the simplified expressions:** - First: $$\frac{3x^3}{2}$$ - Second: $$\frac{3x^4}{2}$$ 5. **Analyze the difference:** The powers of $x$ are different ($x^3$ vs $x^4$), so the expressions are not equivalent. **Final answer:** The expressions $$\frac{3x^3}{2}$$ and $$\frac{6x^4}{4}$$ are **not equivalent** because their powers of $x$ differ.