Simplify cube root of (256x^4)/(4x)

$\sqrt[3]{\frac{256 x^{4}}{4 x}}$

Step 1

Reduce the expression $\frac{256 x^{4}}{4 x}$ by cancelling the common factors.

Factor $4$ out of $256 x^{4}$ .

$\sqrt[3]{\frac{4 (64 x^{4})}{4 x}}$

Factor $4$ out of $4 x$ .

$\sqrt[3]{\frac{4 (64 x^{4})}{4 (x)}}$

Cancel the common factor.

$\sqrt[3]{\frac{4 (64 x^{4})}{4 x}}$

Rewrite the expression.

$\sqrt[3]{\frac{64 x^{4}}{x}}$

Step 2

Cancel the common factor of $x^{4}$ and $x$ .

Factor $x$ out of $64 x^{4}$ .

$\sqrt[3]{\frac{x (64 x^{3})}{x}}$

Cancel the common factors.

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

$\sqrt[3]{\frac{x (64 x^{3})}{x^{1}}}$

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

$\sqrt[3]{\frac{x (64 x^{3})}{x \cdot 1}}$

Cancel the common factor.

$\sqrt[3]{\frac{x (64 x^{3})}{x \cdot 1}}$

Rewrite the expression.

$\sqrt[3]{\frac{64 x^{3}}{1}}$

Divide $64 x^{3}$ by $1$ .

$\sqrt[3]{64 x^{3}}$

Step 3

Rewrite $64 x^{3}$ as ${(4 x)}^{3}$ .

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

Step 4

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

$4 x$