Simplify cube root of (128x^5)/(16x^2)

$\sqrt[3]{\frac{128 x^{5}}{16 x^{2}}}$

Step 1

Reduce the expression $\frac{128 x^{5}}{16 x^{2}}$ by cancelling the common factors.

Factor $16$ out of $128 x^{5}$ .

$\sqrt[3]{\frac{16 (8 x^{5})}{16 x^{2}}}$

Factor $16$ out of $16 x^{2}$ .

$\sqrt[3]{\frac{16 (8 x^{5})}{16 (x^{2})}}$

Cancel the common factor.

$\sqrt[3]{\frac{16 (8 x^{5})}{16 x^{2}}}$

Rewrite the expression.

$\sqrt[3]{\frac{8 x^{5}}{x^{2}}}$

Step 2

Cancel the common factor of $x^{5}$ and $x^{2}$ .

Factor $x^{2}$ out of $8 x^{5}$ .

$\sqrt[3]{\frac{x^{2} (8 x^{3})}{x^{2}}}$

Cancel the common factors.

Multiply by $1$ .

$\sqrt[3]{\frac{x^{2} (8 x^{3})}{x^{2} \cdot 1}}$

Cancel the common factor.

$\sqrt[3]{\frac{x^{2} (8 x^{3})}{x^{2} \cdot 1}}$

Rewrite the expression.

$\sqrt[3]{\frac{8 x^{3}}{1}}$

Divide $8 x^{3}$ by $1$ .

$\sqrt[3]{8 x^{3}}$

Step 3

Rewrite $8 x^{3}$ as ${(2 x)}^{3}$ .

$\sqrt[3]{{(2 x)}^{3}}$

Step 4

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

$2 x$