Simplify ( cube root of 24x^5y^2)/( cube root of 3x^2y)

$\frac{\sqrt[3]{24 x^{5} y^{2}}}{\sqrt[3]{3 x^{2} y}}$

Step 1

Combine $\sqrt[3]{24 x^{5} y^{2}}$ and $\sqrt[3]{3 x^{2} y}$ into a single radical.

$\sqrt[3]{\frac{24 x^{5} y^{2}}{3 x^{2} y}}$

Step 2

Reduce the expression $\frac{24 x^{5} y^{2}}{3 x^{2} y}$ by cancelling the common factors.

Factor $3$ out of $24 x^{5} y^{2}$ .

$\sqrt[3]{\frac{3 (8 x^{5} y^{2})}{3 x^{2} y}}$

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

$\sqrt[3]{\frac{3 (8 x^{5} y^{2})}{3 (x^{2} y)}}$

Cancel the common factor.

$\sqrt[3]{\frac{3 (8 x^{5} y^{2})}{3 (x^{2} y)}}$

Rewrite the expression.

$\sqrt[3]{\frac{8 x^{5} y^{2}}{x^{2} y}}$

Step 3

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

Factor $x^{2}$ out of $8 x^{5} y^{2}$ .

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 4

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

Factor $y$ out of $8 x^{3} y^{2}$ .

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

Cancel the common factors.

Raise $y$ to the power of $1$ .

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

Factor $y$ out of $y^{1}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Divide $8 x^{3} y$ by $1$ .

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

Step 5

Rewrite $8 x^{3} y$ as ${(2 x)}^{3} y$ .

Rewrite $8$ as $2^{3}$ .

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

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

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

Step 6

Pull terms out from under the radical.

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

Simplify ( cube root of 24x^5y^2)/( cube root of 3x^2y)

Related Questions

Support LCMGCF.com by disabling your adblocker.