Simplify fourth root of (1024m^10n^4p^12)/(4m^2p^4)

$\sqrt[4]{\frac{1024 m^{10} n^{4} p^{12}}{4 m^{2} p^{4}}}$

Reduce the expression $\frac{1024 m^{10} n^{4} p^{12}}{4 m^{2} p^{4}}$ by cancelling the common factors.

Factor $4$ out of $1024 m^{10} n^{4} p^{12}$ .

$\sqrt[4]{\frac{4 (256 m^{10} n^{4} p^{12})}{4 m^{2} p^{4}}}$

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

$\sqrt[4]{\frac{4 (256 m^{10} n^{4} p^{12})}{4 (m^{2} p^{4})}}$

Cancel the common factor.

$\sqrt[4]{\frac{4 (256 m^{10} n^{4} p^{12})}{4 (m^{2} p^{4})}}$

Rewrite the expression.

$\sqrt[4]{\frac{256 m^{10} n^{4} p^{12}}{m^{2} p^{4}}}$

Cancel the common factor of $m^{10}$ and $m^{2}$ .

Factor $m^{2}$ out of $256 m^{10} n^{4} p^{12}$ .

$\sqrt[4]{\frac{m^{2} (256 m^{8} n^{4} p^{12})}{m^{2} p^{4}}}$

Cancel the common factors.

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

$\sqrt[4]{\frac{m^{2} (256 m^{8} n^{4} p^{12})}{m^{2} (p^{4})}}$

Cancel the common factor.

$\sqrt[4]{\frac{m^{2} (256 m^{8} n^{4} p^{12})}{m^{2} p^{4}}}$

Rewrite the expression.

$\sqrt[4]{\frac{256 m^{8} n^{4} p^{12}}{p^{4}}}$

Cancel the common factor of $p^{12}$ and $p^{4}$ .

Factor $p^{4}$ out of $256 m^{8} n^{4} p^{12}$ .

$\sqrt[4]{\frac{p^{4} (256 m^{8} n^{4} p^{8})}{p^{4}}}$

Cancel the common factors.

Multiply by $1$ .

$\sqrt[4]{\frac{p^{4} (256 m^{8} n^{4} p^{8})}{p^{4} \cdot 1}}$

Cancel the common factor.

$\sqrt[4]{\frac{p^{4} (256 m^{8} n^{4} p^{8})}{p^{4} \cdot 1}}$

Rewrite the expression.

$\sqrt[4]{\frac{256 m^{8} n^{4} p^{8}}{1}}$

Divide $256 m^{8} n^{4} p^{8}$ by $1$ .

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

Rewrite $256 m^{8} n^{4} p^{8}$ as ${(4 m^{2} n p^{2})}^{4}$ .

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

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

$4 m^{2} n p^{2}$