Simplify ( sixth root of 128x^7)/( sixth root of 2x)

$\frac{\sqrt[6]{128 x^{7}}}{\sqrt[6]{2 x}}$

Step 1

Combine $\sqrt[6]{128 x^{7}}$ and $\sqrt[6]{2 x}$ into a single radical.

$\sqrt[6]{\frac{128 x^{7}}{2 x}}$

Step 2

Reduce the expression $\frac{128 x^{7}}{2 x}$ by cancelling the common factors.

Factor $2$ out of $128 x^{7}$ .

$\sqrt[6]{\frac{2 (64 x^{7})}{2 x}}$

Factor $2$ out of $2 x$ .

$\sqrt[6]{\frac{2 (64 x^{7})}{2 (x)}}$

Cancel the common factor.

$\sqrt[6]{\frac{2 (64 x^{7})}{2 x}}$

Rewrite the expression.

$\sqrt[6]{\frac{64 x^{7}}{x}}$

Step 3

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

Factor $x$ out of $64 x^{7}$ .

$\sqrt[6]{\frac{x (64 x^{6})}{x}}$

Cancel the common factors.

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

$\sqrt[6]{\frac{x (64 x^{6})}{x^{1}}}$

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

$\sqrt[6]{\frac{x (64 x^{6})}{x \cdot 1}}$

Cancel the common factor.

$\sqrt[6]{\frac{x (64 x^{6})}{x \cdot 1}}$

Rewrite the expression.

$\sqrt[6]{\frac{64 x^{6}}{1}}$

Divide $64 x^{6}$ by $1$ .

$\sqrt[6]{64 x^{6}}$

Step 4

Rewrite $64 x^{6}$ as ${(2 x)}^{6}$ .

$\sqrt[6]{{(2 x)}^{6}}$

Step 5

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

$2 x$