Simplify ( fourth root of 162x^5)/( fourth root of 2x)

$\frac{\sqrt[4]{162 x^{5}}}{\sqrt[4]{2 x}}$

Step 1

Combine $\sqrt[4]{162 x^{5}}$ and $\sqrt[4]{2 x}$ into a single radical.

$\sqrt[4]{\frac{162 x^{5}}{2 x}}$

Step 2

Reduce the expression $\frac{162 x^{5}}{2 x}$ by cancelling the common factors.

Factor $2$ out of $162 x^{5}$ .

$\sqrt[4]{\frac{2 (81 x^{5})}{2 x}}$

Factor $2$ out of $2 x$ .

$\sqrt[4]{\frac{2 (81 x^{5})}{2 (x)}}$

Cancel the common factor.

$\sqrt[4]{\frac{2 (81 x^{5})}{2 x}}$

Rewrite the expression.

$\sqrt[4]{\frac{81 x^{5}}{x}}$

Step 3

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

Factor $x$ out of $81 x^{5}$ .

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

Cancel the common factors.

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

$\sqrt[4]{\frac{x (81 x^{4})}{x^{1}}}$

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

$\sqrt[4]{\frac{x (81 x^{4})}{x \cdot 1}}$

Cancel the common factor.

$\sqrt[4]{\frac{x (81 x^{4})}{x \cdot 1}}$

Rewrite the expression.

$\sqrt[4]{\frac{81 x^{4}}{1}}$

Divide $81 x^{4}$ by $1$ .

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

Step 4

Rewrite $81 x^{4}$ as ${(3 x)}^{4}$ .

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

Step 5

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

$3 x$