Simplify ( cube root of 81x^4)/( cube root of 3x)

$\frac{\sqrt[3]{81 x^{4}}}{\sqrt[3]{3 x}}$

Step 1

Combine $\sqrt[3]{81 x^{4}}$ and $\sqrt[3]{3 x}$ into a single radical.

$\sqrt[3]{\frac{81 x^{4}}{3 x}}$

Step 2

Reduce the expression $\frac{81 x^{4}}{3 x}$ by cancelling the common factors.

Factor $3$ out of $81 x^{4}$ .

$\sqrt[3]{\frac{3 (27 x^{4})}{3 x}}$

Factor $3$ out of $3 x$ .

$\sqrt[3]{\frac{3 (27 x^{4})}{3 (x)}}$

Cancel the common factor.

$\sqrt[3]{\frac{3 (27 x^{4})}{3 x}}$

Rewrite the expression.

$\sqrt[3]{\frac{27 x^{4}}{x}}$

Step 3

Cancel the common factor of $x^{4}$ and $x$ .

Factor $x$ out of $27 x^{4}$ .

$\sqrt[3]{\frac{x (27 x^{3})}{x}}$

Cancel the common factors.

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

$\sqrt[3]{\frac{x (27 x^{3})}{x^{1}}}$

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

$\sqrt[3]{\frac{x (27 x^{3})}{x \cdot 1}}$

Cancel the common factor.

$\sqrt[3]{\frac{x (27 x^{3})}{x \cdot 1}}$

Rewrite the expression.

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

Divide $27 x^{3}$ by $1$ .

$\sqrt[3]{27 x^{3}}$

Step 4

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

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

Step 5

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

$3 x$