Finite Math Examples

$\sqrt[5]{x^{5} y^{12} z^{20}}$

Step 1

Rewrite $x^{5} y^{12} z^{20}$ as ${(x y^{2} z^{4})}^{5} y^{2}$ .

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Step 1.1

Factor out $y^{10}$ .

$\sqrt[5]{x^{5} (y^{10} y^{2}) z^{20}}$

Step 1.2

Rewrite $y^{10}$ as ${(y^{2})}^{5}$ .

$\sqrt[5]{x^{5} ({(y^{2})}^{5} y^{2}) z^{20}}$

Step 1.3

Rewrite $z^{20}$ as ${(z^{4})}^{5}$ .

$\sqrt[5]{x^{5} ({(y^{2})}^{5} y^{2}) {(z^{4})}^{5}}$

Step 1.4

Move $y^{2}$ .

$\sqrt[5]{x^{5} ({(y^{2})}^{5}) {(z^{4})}^{5} y^{2}}$

Step 1.5

Rewrite $x^{5} ({(y^{2})}^{5}) {(z^{4})}^{5}$ as ${(x y^{2} z^{4})}^{5}$ .

$\sqrt[5]{{(x y^{2} z^{4})}^{5} y^{2}}$

Step 2

Pull terms out from under the radical.

$x y^{2} z^{4} \sqrt[5]{y^{2}}$