Simplify ( cube root of 243u^10)/( cube root of 3u^2)

$\frac{\sqrt[3]{243 u^{10}}}{\sqrt[3]{3 u^{2}}}$

Step 1

Combine $\sqrt[3]{243 u^{10}}$ and $\sqrt[3]{3 u^{2}}$ into a single radical.

$\sqrt[3]{\frac{243 u^{10}}{3 u^{2}}}$

Step 2

Reduce the expression $\frac{243 u^{10}}{3 u^{2}}$ by cancelling the common factors.

Factor $3$ out of $243 u^{10}$ .

$\sqrt[3]{\frac{3 (81 u^{10})}{3 u^{2}}}$

Factor $3$ out of $3 u^{2}$ .

$\sqrt[3]{\frac{3 (81 u^{10})}{3 (u^{2})}}$

Cancel the common factor.

$\sqrt[3]{\frac{3 (81 u^{10})}{3 u^{2}}}$

Rewrite the expression.

$\sqrt[3]{\frac{81 u^{10}}{u^{2}}}$

Step 3

Cancel the common factor of $u^{10}$ and $u^{2}$ .

Factor $u^{2}$ out of $81 u^{10}$ .

$\sqrt[3]{\frac{u^{2} (81 u^{8})}{u^{2}}}$

Cancel the common factors.

Multiply by $1$ .

$\sqrt[3]{\frac{u^{2} (81 u^{8})}{u^{2} \cdot 1}}$

Cancel the common factor.

$\sqrt[3]{\frac{u^{2} (81 u^{8})}{u^{2} \cdot 1}}$

Rewrite the expression.

$\sqrt[3]{\frac{81 u^{8}}{1}}$

Divide $81 u^{8}$ by $1$ .

$\sqrt[3]{81 u^{8}}$

Step 4

Rewrite $81 u^{8}$ as ${(3 u^{2})}^{3} \cdot (3 u^{2})$ .

Factor $27$ out of $81$ .

$\sqrt[3]{27 (3) u^{8}}$

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

$\sqrt[3]{3^{3} \cdot 3 u^{8}}$

Factor out $u^{6}$ .

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

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

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

Move $3$ .

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

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

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

Add parentheses.

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

Step 5

Pull terms out from under the radical.

$3 u^{2} \sqrt[3]{3 u^{2}}$

Simplify ( cube root of 243u^10)/( cube root of 3u^2)

Related Questions

Support LCMGCF.com by disabling your adblocker.