If the expression (sqrt (4xy^3))/(5x^-1)y^(-(5)/(2)) is written in the form ax^by^c then what is the product of a, b and C? Answer Attempt 2 out of square

To simplify the expression $\frac {\sqrt {4xy^{3}}}{5x^{-1}y^{-\frac {5}{2}}}$, we can start by simplifying the numerator and denominator separately.<br /><br />In the numerator, we have $\sqrt{4xy^3}$. We can simplify this by taking the square root of each term separately:<br /><br />$\sqrt{4xy^3} = \sqrt{4} \cdot \sqrt{x} \cdot \sqrt{y^3} = 2 \cdot \sqrt{x} \cdot y^{\frac{3}{2}}$<br /><br />In the denominator, we have $5x^{-1}y^{-\frac{5}{2}}$. We can simplify this by applying the negative exponent rule:<br /><br />$5x^{-1}y^{-\frac{5}{2}} = 5 \cdot \frac{1}{x} \cdot \frac{1}{y^{\frac{5}{2}}} = \frac{5}{x} \cdot \frac{1}{y^{\frac{5}{2}}} = \frac{5}{xy^{\frac{5}{2}}}$<br /><br />Now, we can rewrite the original expression as:<br /><br />$\frac{2 \cdot \sqrt{x} \cdot y^{\frac{3}{2}}}{\frac{5}{xy^{\frac{5}{2}}}}$<br /><br />To simplify this further, we can multiply the numerator and denominator by $xy^{\frac{5}{2}}$:<br /><br />$\frac{2 \cdot \sqrt{x} \cdot y^{\frac{3}{2}} \cdot xy^{\frac{5}{2}}}{\frac{5}{xy^{\frac{5}{2}}} \cdot xy^{\frac{5}{2}}} = \frac{2 \cdot x \cdot y^{\frac{3}{2} + \frac{5}{2}}}{5} = \frac{2 \cdot x \cdot y^4}{5}$<br /><br />Therefore, the expression can be written in the form $ax^b y^c$ as $\frac{2}{5}x^1y^4$.<br /><br />The product of $a$, $b$, and $c$ is $\frac{2}{5} \cdot 1 \cdot 4 = \frac{8}{5}$.