# How do you rationalize the denominator & simplify: variable with exponents of (9w^9)/(4 sqrt(2z^7))?

$\frac{9 {w}^{9}}{4 \sqrt{2 {z}^{7}}} \cdot \frac{\sqrt{2 {z}^{7}}}{\sqrt{2 {z}^{7}}}$
$= \frac{9 {w}^{9} \cdot {2}^{\frac{1}{2}} \cdot {z}^{\frac{7}{2}}}{4 \cdot 2 \cdot {z}^{7}}$
$= \frac{9 {w}^{9} \cdot {2}^{\frac{1}{2}} \cdot {z}^{\frac{7}{2}}}{8 \cdot {z}^{7}}$
$= \frac{9}{8} \cdot {w}^{9} \cdot \sqrt{2} \cdot {z}^{\frac{7}{2} - 7}$