Simplify ( eighth root of 512x^9)/( eighth root of 2x)

$\frac{\sqrt[8]{512 x^{9}}}{\sqrt[8]{2 x}}$

Step 1

Combine $\sqrt[8]{512 x^{9}}$ and $\sqrt[8]{2 x}$ into a single radical.

$\sqrt[8]{\frac{512 x^{9}}{2 x}}$

Step 2

Reduce the expression $\frac{512 x^{9}}{2 x}$ by cancelling the common factors.

Factor $2$ out of $512 x^{9}$ .

$\sqrt[8]{\frac{2 (256 x^{9})}{2 x}}$

Factor $2$ out of $2 x$ .

$\sqrt[8]{\frac{2 (256 x^{9})}{2 (x)}}$

Cancel the common factor.

$\sqrt[8]{\frac{2 (256 x^{9})}{2 x}}$

Rewrite the expression.

$\sqrt[8]{\frac{256 x^{9}}{x}}$

Step 3

Cancel the common factor of $x^{9}$ and $x$ .

Factor $x$ out of $256 x^{9}$ .

$\sqrt[8]{\frac{x (256 x^{8})}{x}}$

Cancel the common factors.

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

$\sqrt[8]{\frac{x (256 x^{8})}{x^{1}}}$

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

$\sqrt[8]{\frac{x (256 x^{8})}{x \cdot 1}}$

Cancel the common factor.

$\sqrt[8]{\frac{x (256 x^{8})}{x \cdot 1}}$

Rewrite the expression.

$\sqrt[8]{\frac{256 x^{8}}{1}}$

Divide $256 x^{8}$ by $1$ .

$\sqrt[8]{256 x^{8}}$

Step 4

Rewrite $256 x^{8}$ as ${(2 x)}^{8}$ .

$\sqrt[8]{{(2 x)}^{8}}$

Step 5

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

$2 x$