Simplify ( cube root of 27xy)/(xy^(-1/2))

$\frac{\sqrt[3]{27 x y}}{x y^{- \frac{1}{2}}}$

Move $y^{- \frac{1}{2}}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{\sqrt[3]{27 x y} y^{\frac{1}{2}}}{x}$

Simplify the numerator.

Rewrite $27 x y$ as $3^{3} (x y)$ .

Rewrite $27$ as $3^{3}$ .

$\frac{\sqrt[3]{3^{3} x y} y^{\frac{1}{2}}}{x}$

Add parentheses.

$\frac{\sqrt[3]{3^{3} (x y)} y^{\frac{1}{2}}}{x}$

Pull terms out from under the radical.

$\frac{3 \sqrt[3]{x y} y^{\frac{1}{2}}}{x}$