Algebra Examples

$\sqrt[3]{8 x^{4} y^{17}}$

Step 1

Rewrite $8 x^{4} y^{17}$ as ${(2 x y^{5})}^{3} (x y^{2})$ .

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Step 1.1

Rewrite $8$ as $2^{3}$ .

$\sqrt[3]{2^{3} x^{4} y^{17}}$

Step 1.2

Factor out $x^{3}$ .

$\sqrt[3]{2^{3} (x^{3} x) y^{17}}$

Step 1.3

Factor out $y^{15}$ .

$\sqrt[3]{2^{3} (x^{3} x) (y^{15} y^{2})}$

Step 1.4

Rewrite $y^{15}$ as ${(y^{5})}^{3}$ .

$\sqrt[3]{2^{3} (x^{3} x) ({(y^{5})}^{3} y^{2})}$

Step 1.5

Move $x$ .

$\sqrt[3]{2^{3} (x^{3}) {(y^{5})}^{3} x y^{2}}$

Step 1.6

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

$\sqrt[3]{{(2 x y^{5})}^{3} x y^{2}}$

Step 1.7

Add parentheses.

$\sqrt[3]{{(2 x y^{5})}^{3} (x y^{2})}$

Step 2

Pull terms out from under the radical.

$2 x y^{5} \sqrt[3]{x y^{2}}$