Algebra Examples

$\sqrt[4]{81 x^{5} y^{9}}$

Step 1

Rewrite $81 x^{5} y^{9}$ as ${(3 x y^{2})}^{4} (x y)$ .

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Step 1.1

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

$\sqrt[4]{3^{4} x^{5} y^{9}}$

Step 1.2

Factor out $x^{4}$ .

$\sqrt[4]{3^{4} (x^{4} x) y^{9}}$

Step 1.3

Factor out $y^{8}$ .

$\sqrt[4]{3^{4} (x^{4} x) (y^{8} y)}$

Step 1.4

Rewrite $y^{8}$ as ${(y^{2})}^{4}$ .

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

Step 1.5

Move $x$ .

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

Step 1.6

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

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

Step 1.7

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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