Simplify ( fifth root of 729x^6)/( fifth root of 3x)

$\frac{\sqrt[5]{729 x^{6}}}{\sqrt[5]{3 x}}$

Combine $\sqrt[5]{729 x^{6}}$ and $\sqrt[5]{3 x}$ into a single radical.

$\sqrt[5]{\frac{729 x^{6}}{3 x}}$

Reduce the expression $\frac{729 x^{6}}{3 x}$ by cancelling the common factors.

Factor $3$ out of $729 x^{6}$ .

$\sqrt[5]{\frac{3 (243 x^{6})}{3 x}}$

Factor $3$ out of $3 x$ .

$\sqrt[5]{\frac{3 (243 x^{6})}{3 (x)}}$

Cancel the common factor.

$\sqrt[5]{\frac{3 (243 x^{6})}{3 x}}$

Rewrite the expression.

$\sqrt[5]{\frac{243 x^{6}}{x}}$

Cancel the common factor of $x^{6}$ and $x$ .

Factor $x$ out of $243 x^{6}$ .

$\sqrt[5]{\frac{x (243 x^{5})}{x}}$

Cancel the common factors.

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

$\sqrt[5]{\frac{x (243 x^{5})}{x^{1}}}$

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

$\sqrt[5]{\frac{x (243 x^{5})}{x \cdot 1}}$

Cancel the common factor.

$\sqrt[5]{\frac{x (243 x^{5})}{x \cdot 1}}$

Rewrite the expression.

$\sqrt[5]{\frac{243 x^{5}}{1}}$

Divide $243 x^{5}$ by $1$ .

$\sqrt[5]{243 x^{5}}$

Rewrite $243 x^{5}$ as ${(3 x)}^{5}$ .

$\sqrt[5]{{(3 x)}^{5}}$

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

$3 x$