Algebra Examples

$\sqrt[3]{125 x^{10} y^{13}} + \sqrt[3]{27 x^{10} y^{13}}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $125 x^{10} y^{13}$ as ${(5 x^{3} y^{4})}^{3} (x y)$ .

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Step 1.1.1

Rewrite $125$ as $5^{3}$ .

$\sqrt[3]{5^{3} x^{10} y^{13}} + \sqrt[3]{27 x^{10} y^{13}}$

Step 1.1.2

Factor out $x^{9}$ .

$\sqrt[3]{5^{3} (x^{9} x) y^{13}} + \sqrt[3]{27 x^{10} y^{13}}$

Step 1.1.3

Rewrite $x^{9}$ as ${(x^{3})}^{3}$ .

$\sqrt[3]{5^{3} ({(x^{3})}^{3} x) y^{13}} + \sqrt[3]{27 x^{10} y^{13}}$

Step 1.1.4

Factor out $y^{12}$ .

$\sqrt[3]{5^{3} ({(x^{3})}^{3} x) (y^{12} y)} + \sqrt[3]{27 x^{10} y^{13}}$

Step 1.1.5

Rewrite $y^{12}$ as ${(y^{4})}^{3}$ .

$\sqrt[3]{5^{3} ({(x^{3})}^{3} x) ({(y^{4})}^{3} y)} + \sqrt[3]{27 x^{10} y^{13}}$

Step 1.1.6

Move $x$ .

$\sqrt[3]{5^{3} ({(x^{3})}^{3}) {(y^{4})}^{3} x y} + \sqrt[3]{27 x^{10} y^{13}}$

Step 1.1.7

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

$\sqrt[3]{{(5 x^{3} y^{4})}^{3} x y} + \sqrt[3]{27 x^{10} y^{13}}$

Step 1.1.8

Add parentheses.

$\sqrt[3]{{(5 x^{3} y^{4})}^{3} (x y)} + \sqrt[3]{27 x^{10} y^{13}}$

Step 1.2

Pull terms out from under the radical.

$5 x^{3} y^{4} \sqrt[3]{x y} + \sqrt[3]{27 x^{10} y^{13}}$

Step 1.3

Rewrite $27 x^{10} y^{13}$ as ${(3 x^{3} y^{4})}^{3} (x y)$ .

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Step 1.3.1

Rewrite $27$ as $3^{3}$ .

$5 x^{3} y^{4} \sqrt[3]{x y} + \sqrt[3]{3^{3} x^{10} y^{13}}$

Step 1.3.2

Factor out $x^{9}$ .

$5 x^{3} y^{4} \sqrt[3]{x y} + \sqrt[3]{3^{3} (x^{9} x) y^{13}}$

Step 1.3.3

Rewrite $x^{9}$ as ${(x^{3})}^{3}$ .

$5 x^{3} y^{4} \sqrt[3]{x y} + \sqrt[3]{3^{3} ({(x^{3})}^{3} x) y^{13}}$

Step 1.3.4

Factor out $y^{12}$ .

$5 x^{3} y^{4} \sqrt[3]{x y} + \sqrt[3]{3^{3} ({(x^{3})}^{3} x) (y^{12} y)}$

Step 1.3.5

Rewrite $y^{12}$ as ${(y^{4})}^{3}$ .

$5 x^{3} y^{4} \sqrt[3]{x y} + \sqrt[3]{3^{3} ({(x^{3})}^{3} x) ({(y^{4})}^{3} y)}$

Step 1.3.6

Move $x$ .

$5 x^{3} y^{4} \sqrt[3]{x y} + \sqrt[3]{3^{3} ({(x^{3})}^{3}) {(y^{4})}^{3} x y}$

Step 1.3.7

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

$5 x^{3} y^{4} \sqrt[3]{x y} + \sqrt[3]{{(3 x^{3} y^{4})}^{3} x y}$

Step 1.3.8

Add parentheses.

$5 x^{3} y^{4} \sqrt[3]{x y} + \sqrt[3]{{(3 x^{3} y^{4})}^{3} (x y)}$

Step 1.4

Pull terms out from under the radical.

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

Step 2

Add $5 x^{3} y^{4} \sqrt[3]{x y}$ and $3 x^{3} y^{4} \sqrt[3]{x y}$ .

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