Question: Simplify the expression $$\frac{2x^4y}{3x^2} \cdot \frac{4xy^3}{2x^3y^2}$$ at a math 1 level.
1. **State the problem:** Simplify the expression $$\frac{2x^4y}{3x^2} \cdot \frac{4xy^3}{2x^3y^2}$$.
2. **Rewrite the expression:**
$$\frac{2x^4y}{3x^2} \times \frac{4xy^3}{2x^3y^2}$$
3. **Multiply the numerators and denominators:**
$$\frac{2x^4y \times 4xy^3}{3x^2 \times 2x^3y^2} = \frac{8x^{4+1}y^{1+3}}{6x^{2+3}y^2} = \frac{8x^5y^4}{6x^5y^2}$$
4. **Simplify the fraction by canceling common factors:**
$$\frac{\cancel{8}^\frac{4}{3}x^5y^4}{\cancel{6}^2x^5y^2} = \frac{4}{3} \times \frac{\cancel{x^5}}{\cancel{x^5}} \times \frac{y^4}{y^2} = \frac{4}{3} y^{4-2} = \frac{4}{3} y^2$$
5. **Final simplified expression:**
$$\frac{4}{3} y^2$$
**Explanation:**
- When multiplying fractions, multiply numerators and denominators separately.
- Use the rule $$x^a \times x^b = x^{a+b}$$ to combine powers.
- When dividing like bases, subtract exponents: $$\frac{x^a}{x^b} = x^{a-b}$$.
- Cancel common factors to simplify the fraction.
- The final answer is $$\frac{4}{3} y^2$$.