Simplify fourth root of (243x^3)/(3x^7)

$\sqrt[4]{\frac{243 x^{3}}{3 x^{7}}}$

Reduce the expression $\frac{243 x^{3}}{3 x^{7}}$ by cancelling the common factors.

Factor $3$ out of $243 x^{3}$ .

$\sqrt[4]{\frac{3 (81 x^{3})}{3 x^{7}}}$

Factor $3$ out of $3 x^{7}$ .

$\sqrt[4]{\frac{3 (81 x^{3})}{3 (x^{7})}}$

Cancel the common factor.

$\sqrt[4]{\frac{3 (81 x^{3})}{3 x^{7}}}$

Rewrite the expression.

$\sqrt[4]{\frac{81 x^{3}}{x^{7}}}$

Cancel the common factor of $x^{3}$ and $x^{7}$ .

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

$\sqrt[4]{\frac{x^{3} \cdot 81}{x^{7}}}$

Cancel the common factors.

Factor $x^{3}$ out of $x^{7}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Rewrite $81$ as $3^{4}$ .

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

Rewrite $\frac{3^{4}}{x^{4}}$ as ${(\frac{3}{x})}^{4}$ .

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

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

$\frac{3}{x}$