Simplify (6 cube root of x^7y^5)÷2 cube root of xy^2

$6 \sqrt[3]{x^{7} y^{5}} \div 2 \sqrt[3]{x y^{2}}$

Rewrite the division as a fraction.

$\frac{6 \sqrt[3]{x^{7} y^{5}}}{2 \sqrt[3]{x y^{2}}}$

Cancel the common factor of $6$ and $2$ .

Factor $2$ out of $6 \sqrt[3]{x^{7} y^{5}}$ .

$\frac{2 (3 \sqrt[3]{x^{7} y^{5}})}{2 \sqrt[3]{x y^{2}}}$

Cancel the common factors.

Factor $2$ out of $2 \sqrt[3]{x y^{2}}$ .

$\frac{2 (3 \sqrt[3]{x^{7} y^{5}})}{2 (\sqrt[3]{x y^{2}})}$

Cancel the common factor.

$\frac{2 (3 \sqrt[3]{x^{7} y^{5}})}{2 \sqrt[3]{x y^{2}}}$

Rewrite the expression.

$\frac{3 \sqrt[3]{x^{7} y^{5}}}{\sqrt[3]{x y^{2}}}$

Combine $\sqrt[3]{x^{7} y^{5}}$ and $\sqrt[3]{x y^{2}}$ into a single radical.

$3 \sqrt[3]{\frac{x^{7} y^{5}}{x y^{2}}}$

Reduce the expression $\frac{x^{7} y^{5}}{x y^{2}}$ by cancelling the common factors.

Factor $x$ out of $x^{7} y^{5}$ .

$3 \sqrt[3]{\frac{x (x^{6} y^{5})}{x y^{2}}}$

Factor $x$ out of $x y^{2}$ .

$3 \sqrt[3]{\frac{x (x^{6} y^{5})}{x (y^{2})}}$

Cancel the common factor.

$3 \sqrt[3]{\frac{x (x^{6} y^{5})}{x y^{2}}}$

Rewrite the expression.

$3 \sqrt[3]{\frac{x^{6} y^{5}}{y^{2}}}$

Cancel the common factor of $y^{5}$ and $y^{2}$ .

Factor $y^{2}$ out of $x^{6} y^{5}$ .

$3 \sqrt[3]{\frac{y^{2} (x^{6} y^{3})}{y^{2}}}$

Cancel the common factors.

Multiply by $1$ .

$3 \sqrt[3]{\frac{y^{2} (x^{6} y^{3})}{y^{2} \cdot 1}}$

Cancel the common factor.

$3 \sqrt[3]{\frac{y^{2} (x^{6} y^{3})}{y^{2} \cdot 1}}$

Rewrite the expression.

$3 \sqrt[3]{\frac{x^{6} y^{3}}{1}}$

Divide $x^{6} y^{3}$ by $1$ .

$3 \sqrt[3]{x^{6} y^{3}}$

Rewrite $x^{6} y^{3}$ as ${(x^{2} y)}^{3}$ .

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

Pull terms out from under the radical, assuming real numbers.

$3 x^{2} y$