If the expression (sqrt (16x^3y^5))/(x^frac (1)(2)y^2) is written in the form ax^by^c , then what is the product of a, b and c? Answer Attemptiont of 2 square

To simplify the expression $\frac {\sqrt {16x^{3}y^{5}}}{x^{\frac {1}{2}}y^{2}}$, we can follow these steps:<br /><br />1. Simplify the numerator:<br /> $\sqrt{16x^{3}y^{5}} = \sqrt{16} \cdot \sqrt{x^{3}} \cdot \sqrt{y^{5}} = 4x^{\frac{3}{2}}y^{\frac{5}{2}}$<br /><br />2. Simplify the denominator:<br /> $x^{\frac{1}{2}}y^{2}$<br /><br />3. Divide the numerator by the denominator:<br /> $\frac{4x^{\frac{3}{2}}y^{\frac{5}{2}}}{x^{\frac{1}{2}}y^{2}} = 4x^{\frac{3}{2} - \frac{1}{2}}y^{\frac{5}{2} - 2} = 4x^{1}y^{\frac{1}{2}}$<br /><br />Therefore, the expression can be written in the form $ax^{b}y^{c}$, where $a = 4$, $b = 1$, and $c = \frac{1}{2}$.<br /><br />The product of $a$, $b$, and $c$ is $4 \cdot 1 \cdot \frac{1}{2} = 2$.<br /><br />So, the answer is $\boxed{2}$.