Given \( x>0 \) and \( y>0 \), select the expression that is equivalent to \[ \sqrt{16 x^{7} y^{11}} \] Answer \( \begin{array}{ll}8 x^{\frac{2}{7}} y^{\frac{2}{11}} & 4 x^{\frac{2}{7}} y^{\frac{2}{11}} \\ 4 x^{\frac{7}{2}} y^{\frac{11}{2}} & 8 x^{\frac{7}{2}} y^{\frac{11}{2}}\end{array} \)

To simplify the expression \( \sqrt{16 x^{7} y^{11}} \), we can break it down into its components. 1. The square root of 16 is 4 (\( \sqrt{16} = 4 \)). 2. The square root of \( x^7 \) is \( x^{7/2} \) (using the property \( \sqrt{x^n} = x^{n/2} \)). 3. The square root of \( y^{11} \) is \( y^{11/2} \) (similarly, \( \sqrt{y^n} = y^{n/2} \)). Thus, combining all parts, we have: \[ \sqrt{16 x^{7} y^{11}} = 4 x^{7/2} y^{11/2} \] The correct equivalent expression is \( 4 x^{\frac{7}{2}} y^{\frac{11}{2}} \).