Algebra Examples

$\sqrt[6]{125 x^{9} y^{6}}$

Step 1

Rewrite $125 x^{9} y^{6}$ as ${(x y)}^{6} \cdot (125 x^{3})$ .

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Step 1.1

Factor out $x^{6}$ .

$\sqrt[6]{125 (x^{6} x^{3}) y^{6}}$

Step 1.2

Move $x^{3}$ .

$\sqrt[6]{125 (x^{6}) y^{6} x^{3}}$

Step 1.3

Move $125$ .

$\sqrt[6]{(x^{6}) y^{6} \cdot 125 x^{3}}$

Step 1.4

Rewrite $(x^{6}) y^{6}$ as ${(x y)}^{6}$ .

$\sqrt[6]{{(x y)}^{6} \cdot 125 x^{3}}$

Step 1.5

Add parentheses.

$\sqrt[6]{{(x y)}^{6} \cdot (125 x^{3})}$

Step 2

Pull terms out from under the radical.

$| x y | \sqrt[6]{125 x^{3}}$

Step 3

Rewrite $125 x^{3}$ as ${(5 x)}^{3}$ .

$| x y | \sqrt[6]{{(5 x)}^{3}}$

Step 4

Rewrite $\sqrt[6]{{(5 x)}^{3}}$ as $\sqrt{\sqrt[3]{{(5 x)}^{3}}}$ .

$| x y | \sqrt{\sqrt[3]{{(5 x)}^{3}}}$

Step 5

Pull terms out from under the radical.

$| x y | \sqrt{5 x}$