Algebra Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

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

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

Step 1.3

Cancel the common factor.

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

Step 1.4

Rewrite the expression.

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

Step 2

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

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Step 2.1

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

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

Step 2.2

Cancel the common factors.

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Step 2.2.1

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

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

Step 2.2.2

Cancel the common factor.

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

Step 2.2.3

Rewrite the expression.

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

Step 3

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

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Step 3.1

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

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

Step 3.2

Cancel the common factors.

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Step 3.2.1

Multiply by $1$ .

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

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

Step 3.2.4

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

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

Step 4

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

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Step 4.1

Factor $16$ out of $128$ .

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

Step 4.2

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

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

Step 4.3

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

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

Step 4.4

Move $8$ .

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

Step 4.5

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

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

Step 5

Pull terms out from under the radical.

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

Step 6

Remove non-negative terms from the absolute value.

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