Question Fully simplify using only positive exponents. \[ \frac{25 x^{5} y^{2}}{x^{8} y^{3}} \]

To simplify the expression \(\frac{25 x^{5} y^{2}}{x^{8} y^{3}}\), we can start by dividing the coefficients and the variables separately. The coefficient is simply \(25\), and since there's no number in the denominator, it remains \(25\). Next, we can apply the quotient rule for exponents, which states that \(\frac{a^m}{a^n} = a^{m-n}\). For the \(x\) terms, we have: \[ \frac{x^{5}}{x^{8}} = x^{5-8} = x^{-3} = \frac{1}{x^3} \] For the \(y\) terms, we do the same: \[ \frac{y^{2}}{y^{3}} = y^{2-3} = y^{-1} = \frac{1}{y} \] Putting it all together, we get: \[ \frac{25 x^{5} y^{2}}{x^{8} y^{3}} = 25 \cdot \frac{1}{x^3} \cdot \frac{1}{y} = \frac{25}{x^{3} y} \] So, the fully simplified expression is: \[ \frac{25}{x^3 y} \]