Simplify cube root of (108x^9y^10)/(2xy^3)

$\sqrt[3]{\frac{108 x^{9} y^{10}}{2 x y^{3}}}$

Step 1

Reduce the expression $\frac{108 x^{9} y^{10}}{2 x y^{3}}$ by cancelling the common factors.

Factor $2$ out of $108 x^{9} y^{10}$ .

$\sqrt[3]{\frac{2 (54 x^{9} y^{10})}{2 x y^{3}}}$

Factor $2$ out of $2 x y^{3}$ .

$\sqrt[3]{\frac{2 (54 x^{9} y^{10})}{2 (x y^{3})}}$

Cancel the common factor.

$\sqrt[3]{\frac{2 (54 x^{9} y^{10})}{2 (x y^{3})}}$

Rewrite the expression.

$\sqrt[3]{\frac{54 x^{9} y^{10}}{x y^{3}}}$

Step 2

Cancel the common factor of $x^{9}$ and $x$ .

Factor $x$ out of $54 x^{9} y^{10}$ .

$\sqrt[3]{\frac{x (54 x^{8} y^{10})}{x y^{3}}}$

Cancel the common factors.

Factor $x$ out of $x y^{3}$ .

$\sqrt[3]{\frac{x (54 x^{8} y^{10})}{x (y^{3})}}$

Cancel the common factor.

$\sqrt[3]{\frac{x (54 x^{8} y^{10})}{x y^{3}}}$

Rewrite the expression.

$\sqrt[3]{\frac{54 x^{8} y^{10}}{y^{3}}}$

Step 3

Cancel the common factor of $y^{10}$ and $y^{3}$ .

Factor $y^{3}$ out of $54 x^{8} y^{10}$ .

$\sqrt[3]{\frac{y^{3} (54 x^{8} y^{7})}{y^{3}}}$

Cancel the common factors.

Multiply by $1$ .

$\sqrt[3]{\frac{y^{3} (54 x^{8} y^{7})}{y^{3} \cdot 1}}$

Cancel the common factor.

$\sqrt[3]{\frac{y^{3} (54 x^{8} y^{7})}{y^{3} \cdot 1}}$

Rewrite the expression.

$\sqrt[3]{\frac{54 x^{8} y^{7}}{1}}$

Divide $54 x^{8} y^{7}$ by $1$ .

$\sqrt[3]{54 x^{8} y^{7}}$

Step 4

Rewrite $54 x^{8} y^{7}$ as ${(3 x^{2} y^{2})}^{3} \cdot (2 x^{2} y)$ .

Factor $27$ out of $54$ .

$\sqrt[3]{27 (2) x^{8} y^{7}}$

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

$\sqrt[3]{3^{3} \cdot 2 x^{8} y^{7}}$

Factor out $x^{6}$ .

$\sqrt[3]{3^{3} \cdot 2 (x^{6} x^{2}) y^{7}}$

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

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

Factor out $y^{6}$ .

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

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

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

Move $x^{2}$ .

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

Move $2$ .

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

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

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

Add parentheses.

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

Add parentheses.

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

Step 5

Pull terms out from under the radical.

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

Simplify cube root of (108x^9y^10)/(2xy^3)

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