If the expression (sqrt (9x^5y))/(6x^frac (3)(2)y^(7)/(2)) is written in the form ax^by^c then what is the product of a, b and C? Answer Attemptiout of 2 square

## Step 1<br />The given expression is \(\frac {\sqrt {9x^{5}y}}{6x^{\frac {3}{2}}y^{\frac {7}{2}}}\). We need to simplify this expression and write it in the form \(ax^{b}y^{c}\).<br /><br />## Step 2<br />First, we simplify the numerator of the expression. The square root of \(9x^{5}y\) can be written as \(\sqrt{9} \sqrt{x^{5}} \sqrt{y}\), which simplifies to \(3x^{2.5}y^{0.5}\).<br /><br />## Step 3<br />Next, we simplify the denominator of the expression. \(6x^{\frac {3}{2}}y^{\frac {7}{2}}\) remains as it is.<br /><br />## Step 4<br />Now, we divide the numerator by the denominator. This gives us \(\frac{3x^{2.5}y^{0.5}}{6x^{\frac {3}{2}}y^{\frac {7}{2}}}\).<br /><br />## Step 5<br />We can simplify this further by dividing the coefficients and the powers of x and y separately. This gives us \(\frac{1}{2}x^{2.5-\frac {3}{2}}y^{0.5-\frac {7}{2}}\).<br /><br />## Step 6<br />Finally, we simplify the powers of x and y to get \(\frac{1}{2}x^{0.5}y^{-\frac {6}{2}}\).<br /><br />## Step 7<br />The final step is to multiply the coefficients a, b, and c together. This gives us \(\frac{1}{2} \times 0.5 \times -\frac {6}{2} = -\frac {3}{4}\).