Simplify ( fifth root of 64x^6)/( fifth root of 2x)

$\frac{\sqrt[5]{64 x^{6}}}{\sqrt[5]{2 x}}$

Step 1

Combine $\sqrt[5]{64 x^{6}}$ and $\sqrt[5]{2 x}$ into a single radical.

$\sqrt[5]{\frac{64 x^{6}}{2 x}}$

Step 2

Reduce the expression $\frac{64 x^{6}}{2 x}$ by cancelling the common factors.

Factor $2$ out of $64 x^{6}$ .

$\sqrt[5]{\frac{2 (32 x^{6})}{2 x}}$

Factor $2$ out of $2 x$ .

$\sqrt[5]{\frac{2 (32 x^{6})}{2 (x)}}$

Cancel the common factor.

$\sqrt[5]{\frac{2 (32 x^{6})}{2 x}}$

Rewrite the expression.

$\sqrt[5]{\frac{32 x^{6}}{x}}$

Step 3

Cancel the common factor of $x^{6}$ and $x$ .

Factor $x$ out of $32 x^{6}$ .

$\sqrt[5]{\frac{x (32 x^{5})}{x}}$

Cancel the common factors.

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

$\sqrt[5]{\frac{x (32 x^{5})}{x^{1}}}$

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

$\sqrt[5]{\frac{x (32 x^{5})}{x \cdot 1}}$

Cancel the common factor.

$\sqrt[5]{\frac{x (32 x^{5})}{x \cdot 1}}$

Rewrite the expression.

$\sqrt[5]{\frac{32 x^{5}}{1}}$

Divide $32 x^{5}$ by $1$ .

$\sqrt[5]{32 x^{5}}$

Step 4

Rewrite $32 x^{5}$ as ${(2 x)}^{5}$ .

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

Step 5

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

$2 x$