1. The problem is to simplify the expression $$10x \div \frac{x^2}{y}$$. 2. Recall that dividing by a fraction is the same as multiplying by its reciprocal. So, $$10x \div \frac{x^2}{y} = 10x \times \frac{y}{x^2}$$. 3. Multiply the numerators and denominators: $$= \frac{10x \times y}{x^2} = \frac{10xy}{x^2}$$. 4. Simplify the fraction by canceling common factors. Since $x^2 = x \times x$, one $x$ cancels with the numerator: $$= \frac{10y}{x}$$. 5. The simplified expression is $$\frac{10y}{x}$$. 6. Comparing with the options given, this matches Option 2. Therefore, the correct simplified form is Option 2: $$\frac{10y}{x}$$.