Finite Math Examples

$\sqrt[6]{256 x^{8} y^{4} z^{10}}$

Step 1

Rewrite $256 x^{8} y^{4} z^{10}$ as ${(2 x z)}^{6} \cdot (4 x^{2} y^{4} z^{4})$ .

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Step 1.1

Factor $64$ out of $256$ .

$\sqrt[6]{64 (4) x^{8} y^{4} z^{10}}$

Step 1.2

Rewrite $64$ as $2^{6}$ .

$\sqrt[6]{2^{6} \cdot 4 x^{8} y^{4} z^{10}}$

Step 1.3

Factor out $x^{6}$ .

$\sqrt[6]{2^{6} \cdot 4 (x^{6} x^{2}) y^{4} z^{10}}$

Step 1.4

Factor out $z^{6}$ .

$\sqrt[6]{2^{6} \cdot 4 (x^{6} x^{2}) y^{4} (z^{6} z^{4})}$

Step 1.5

Move $y^{4}$ .

$\sqrt[6]{2^{6} \cdot 4 (x^{6} x^{2}) z^{6} y^{4} z^{4}}$

Step 1.6

Move $x^{2}$ .

$\sqrt[6]{2^{6} \cdot 4 (x^{6}) z^{6} x^{2} y^{4} z^{4}}$

Step 1.7

Move $4$ .

$\sqrt[6]{(2^{6} (x^{6})) z^{6} \cdot 4 x^{2} y^{4} z^{4}}$

Step 1.8

Rewrite $(2^{6} (x^{6})) z^{6}$ as ${(2 x z)}^{6}$ .

$\sqrt[6]{{(2 x z)}^{6} \cdot 4 x^{2} y^{4} z^{4}}$

Step 1.9

Add parentheses.

$\sqrt[6]{{(2 x z)}^{6} \cdot 4 x^{2} (y^{4} z^{4})}$

Step 1.10

Add parentheses.

$\sqrt[6]{{(2 x z)}^{6} \cdot 4 (x^{2} (y^{4} z^{4}))}$

Step 1.11

Add parentheses.

$\sqrt[6]{{(2 x z)}^{6} \cdot (4 x^{2} y^{4} z^{4})}$

Step 2

Pull terms out from under the radical.

$2 x z \sqrt[6]{4 x^{2} y^{4} z^{4}}$

Step 3

Rewrite $4 x^{2} y^{4} z^{4}$ as ${(2 x y^{2} z^{2})}^{2}$ .

$2 x z \sqrt[6]{{(2 x y^{2} z^{2})}^{2}}$

Step 4

Rewrite $\sqrt[6]{{(2 x y^{2} z^{2})}^{2}}$ as $\sqrt[3]{\sqrt{{(2 x y^{2} z^{2})}^{2}}}$ .

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

Step 5

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

$2 x z \sqrt[3]{2 x y^{2} z^{2}}$