Algebra Examples

$\sqrt[4]{81 x^{6} y^{18}}$

Step 1

Rewrite $81 x^{6} y^{18}$ as ${(3 x y^{4})}^{4} (x^{2} y^{2})$ .

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Step 1.1

Rewrite $81$ as $3^{4}$ .

$\sqrt[4]{3^{4} x^{6} y^{18}}$

Step 1.2

Factor out $x^{4}$ .

$\sqrt[4]{3^{4} (x^{4} x^{2}) y^{18}}$

Step 1.3

Factor out $y^{16}$ .

$\sqrt[4]{3^{4} (x^{4} x^{2}) (y^{16} y^{2})}$

Step 1.4

Rewrite $y^{16}$ as ${(y^{4})}^{4}$ .

$\sqrt[4]{3^{4} (x^{4} x^{2}) ({(y^{4})}^{4} y^{2})}$

Step 1.5

Move $x^{2}$ .

$\sqrt[4]{3^{4} (x^{4}) {(y^{4})}^{4} x^{2} y^{2}}$

Step 1.6

Rewrite $3^{4} (x^{4}) {(y^{4})}^{4}$ as ${(3 x y^{4})}^{4}$ .

$\sqrt[4]{{(3 x y^{4})}^{4} x^{2} y^{2}}$

Step 1.7

Add parentheses.

$\sqrt[4]{{(3 x y^{4})}^{4} (x^{2} y^{2})}$

Step 2

Pull terms out from under the radical.

$| 3 x y^{4} | \sqrt[4]{x^{2} y^{2}}$

Step 3

Remove non-negative terms from the absolute value.

$3 y^{4} | x | \sqrt[4]{x^{2} y^{2}}$

Step 4

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

$3 y^{4} | x | \sqrt[4]{{(x y)}^{2}}$

Step 5

Rewrite $\sqrt[4]{{(x y)}^{2}}$ as $\sqrt{\sqrt{{(x y)}^{2}}}$ .

$3 y^{4} | x | \sqrt{\sqrt{{(x y)}^{2}}}$

Step 6

Pull terms out from under the radical.

$3 y^{4} | x | \sqrt{| x y |}$