Simplify the Radical Expression ( seventh root of 256x^8)/( seventh root of 2x)

$\frac{\sqrt[7]{256 x^{8}}}{\sqrt[7]{2 x}}$

Step 1

Combine $\sqrt[7]{256 x^{8}}$ and $\sqrt[7]{2 x}$ into a single radical.

$\sqrt[7]{\frac{256 x^{8}}{2 x}}$

Step 2

Reduce the expression $\frac{256 x^{8}}{2 x}$ by cancelling the common factors.

Factor $2$ out of $256 x^{8}$ .

$\sqrt[7]{\frac{2 (128 x^{8})}{2 x}}$

Factor $2$ out of $2 x$ .

$\sqrt[7]{\frac{2 (128 x^{8})}{2 (x)}}$

Cancel the common factor.

$\sqrt[7]{\frac{2 (128 x^{8})}{2 x}}$

Rewrite the expression.

$\sqrt[7]{\frac{128 x^{8}}{x}}$

Step 3

Cancel the common factor of $x^{8}$ and $x$ .

Factor $x$ out of $128 x^{8}$ .

$\sqrt[7]{\frac{x (128 x^{7})}{x}}$

Cancel the common factors.

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

$\sqrt[7]{\frac{x (128 x^{7})}{x^{1}}}$

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

$\sqrt[7]{\frac{x (128 x^{7})}{x \cdot 1}}$

Cancel the common factor.

$\sqrt[7]{\frac{x (128 x^{7})}{x \cdot 1}}$

Rewrite the expression.

$\sqrt[7]{\frac{128 x^{7}}{1}}$

Divide $128 x^{7}$ by $1$ .

$\sqrt[7]{128 x^{7}}$

Step 4

Rewrite $128 x^{7}$ as ${(2 x)}^{7}$ .

$\sqrt[7]{{(2 x)}^{7}}$

Step 5

Pull terms out from under the radical.

$2 x$