1. **State the problem:** Simplify the expression $$\frac{6x^{10}y}{2x^{7}y^{3}}$$ using properties of exponents. 2. **Recall the properties of exponents:** - When dividing like bases, subtract the exponents: $$\frac{a^{m}}{a^{n}} = a^{m-n}$$ - Coefficients (numbers) can be divided normally. 3. **Divide the coefficients:** $$\frac{6}{2} = 3$$ 4. **Divide the variables with exponents:** $$\frac{x^{10}}{x^{7}} = x^{10-7} = x^{3}$$ $$\frac{y^{1}}{y^{3}} = y^{1-3} = y^{-2}$$ 5. **Rewrite the expression:** $$3x^{3}y^{-2}$$ 6. **Express negative exponent as a positive exponent in the denominator:** $$3x^{3} \times \frac{1}{y^{2}} = \frac{3x^{3}}{y^{2}}$$ 7. **Final simplified expression:** $$\frac{3x^{3}}{y^{2}}$$ This matches option A.