Simplify fourth root of (256m^8n^4p^16)/(2m^4p^4)

$\sqrt[4]{\frac{256 m^{8} n^{4} p^{16}}{2 m^{4} p^{4}}}$

Reduce the expression $\frac{256 m^{8} n^{4} p^{16}}{2 m^{4} p^{4}}$ by cancelling the common factors.

Factor $2$ out of $256 m^{8} n^{4} p^{16}$ .

$\sqrt[4]{\frac{2 (128 m^{8} n^{4} p^{16})}{2 m^{4} p^{4}}}$

Factor $2$ out of $2 m^{4} p^{4}$ .

$\sqrt[4]{\frac{2 (128 m^{8} n^{4} p^{16})}{2 (m^{4} p^{4})}}$

Cancel the common factor.

$\sqrt[4]{\frac{2 (128 m^{8} n^{4} p^{16})}{2 (m^{4} p^{4})}}$

Rewrite the expression.

$\sqrt[4]{\frac{128 m^{8} n^{4} p^{16}}{m^{4} p^{4}}}$

Cancel the common factor of $m^{8}$ and $m^{4}$ .

Factor $m^{4}$ out of $128 m^{8} n^{4} p^{16}$ .

$\sqrt[4]{\frac{m^{4} (128 m^{4} n^{4} p^{16})}{m^{4} p^{4}}}$

Cancel the common factors.

Factor $m^{4}$ out of $m^{4} p^{4}$ .

$\sqrt[4]{\frac{m^{4} (128 m^{4} n^{4} p^{16})}{m^{4} (p^{4})}}$

Cancel the common factor.

$\sqrt[4]{\frac{m^{4} (128 m^{4} n^{4} p^{16})}{m^{4} p^{4}}}$

Rewrite the expression.

$\sqrt[4]{\frac{128 m^{4} n^{4} p^{16}}{p^{4}}}$

Cancel the common factor of $p^{16}$ and $p^{4}$ .

Factor $p^{4}$ out of $128 m^{4} n^{4} p^{16}$ .

$\sqrt[4]{\frac{p^{4} (128 m^{4} n^{4} p^{12})}{p^{4}}}$

Cancel the common factors.

Multiply by $1$ .

$\sqrt[4]{\frac{p^{4} (128 m^{4} n^{4} p^{12})}{p^{4} \cdot 1}}$

Cancel the common factor.

$\sqrt[4]{\frac{p^{4} (128 m^{4} n^{4} p^{12})}{p^{4} \cdot 1}}$

Rewrite the expression.

$\sqrt[4]{\frac{128 m^{4} n^{4} p^{12}}{1}}$

Divide $128 m^{4} n^{4} p^{12}$ by $1$ .

$\sqrt[4]{128 m^{4} n^{4} p^{12}}$

Rewrite $128 m^{4} n^{4} p^{12}$ as ${(2 m n p^{3})}^{4} \cdot 8$ .

Factor $16$ out of $128$ .

$\sqrt[4]{16 (8) m^{4} n^{4} p^{12}}$

Rewrite $16$ as $2^{4}$ .

$\sqrt[4]{2^{4} \cdot 8 m^{4} n^{4} p^{12}}$

Rewrite $p^{12}$ as ${(p^{3})}^{4}$ .

$\sqrt[4]{2^{4} \cdot 8 m^{4} n^{4} {(p^{3})}^{4}}$

Move $8$ .

$\sqrt[4]{2^{4} m^{4} n^{4} {(p^{3})}^{4} \cdot 8}$

Rewrite $2^{4} m^{4} n^{4} {(p^{3})}^{4}$ as ${(2 m n p^{3})}^{4}$ .

$\sqrt[4]{{(2 m n p^{3})}^{4} \cdot 8}$

Pull terms out from under the radical.

$2 m n p^{3} \sqrt[4]{8}$