If the expression (sqrt [3](27xy^3))/(5x^frac (4)(3)y^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 \(\frac {\sqrt [3]{27xy^{3}}}{5x^{\frac {4}{3}}y^{2}}\). 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 cube root of \(27xy^{3}\) is \(3xy\), because \(27 = 3^3\) and \(y^{3}\) is the cube of \(y\).<br /><br />## Step 3<br />Next, we simplify the denominator of the expression. The denominator is \(5x^{\frac {4}{3}}y^{2}\).<br /><br />## Step 4<br />Now, we divide the numerator by the denominator. This gives us \(\frac {3xy}{5x^{\frac {4}{3}}y^{2}}\).<br /><br />## Step 5<br />We can simplify this further by dividing the terms with the same base. This gives us \(\frac {3}{5}x^{1-\frac {4}{3}}y^{1-2}\).<br /><br />## Step 6<br />Simplifying the exponents gives us \(\frac {3}{5}x^{-\frac {1}{3}}y^{-1}\).<br /><br />## Step 7<br />Finally, we rewrite this in the form \(ax^{b}y^{c}\), which gives us \(\frac {3}{5}x^{-\frac {1}{3}}y^{-1}\).<br /><br />## Step 8<br />The product of \(a\), \(b\), and \(c\) is \(\frac {3}{5}*(-\frac {1}{3})*(-1) = 1\).