Fully simplify using only positive exponents. \[ \frac{27 x y^{3}}{3 x^{8} y^{7}} \]

To simplify the expression \( \frac{27 x y^{3}}{3 x^{8} y^{7}} \), we can start by simplifying the coefficients and then the variables separately. 1. **Coefficients**: Divide \( 27 \) by \( 3 \): \[ \frac{27}{3} = 9 \] 2. **For \( x \)**: Using the property of exponents \( \frac{x^a}{x^b} = x^{a-b} \): \[ \frac{x^1}{x^8} = x^{1-8} = x^{-7} \] 3. **For \( y \)**: Similarly, \[ \frac{y^3}{y^7} = y^{3-7} = y^{-4} \] Putting it all together, we get: \[ \frac{27 x y^{3}}{3 x^{8} y^{7}} = 9 x^{-7} y^{-4} \] Now, to express it using only positive exponents, we can rewrite the negative exponents: \[ 9 x^{-7} y^{-4} = \frac{9}{x^{7} y^{4}} \] So, the fully simplified form is: \[ \frac{9}{x^{7} y^{4}} \]