Finite Math Examples

$\sqrt[3]{54 x^{12} y^{23}}$

Step 1

Rewrite $54 x^{12} y^{23}$ as ${(3 x^{4} y^{7})}^{3} \cdot (2 y^{2})$ .

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Step 1.1

Factor $27$ out of $54$ .

$\sqrt[3]{27 (2) x^{12} y^{23}}$

Step 1.2

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

$\sqrt[3]{3^{3} \cdot 2 x^{12} y^{23}}$

Step 1.3

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

$\sqrt[3]{3^{3} \cdot 2 {(x^{4})}^{3} y^{23}}$

Step 1.4

Factor out $y^{21}$ .

$\sqrt[3]{3^{3} \cdot 2 {(x^{4})}^{3} (y^{21} y^{2})}$

Step 1.5

Rewrite $y^{21}$ as ${(y^{7})}^{3}$ .

$\sqrt[3]{3^{3} \cdot 2 {(x^{4})}^{3} ({(y^{7})}^{3} y^{2})}$

Step 1.6

Move $2$ .

$\sqrt[3]{3^{3} {(x^{4})}^{3} {(y^{7})}^{3} \cdot 2 y^{2}}$

Step 1.7

Rewrite $3^{3} {(x^{4})}^{3} {(y^{7})}^{3}$ as ${(3 x^{4} y^{7})}^{3}$ .

$\sqrt[3]{{(3 x^{4} y^{7})}^{3} \cdot 2 y^{2}}$

Step 1.8

Add parentheses.

$\sqrt[3]{{(3 x^{4} y^{7})}^{3} \cdot (2 y^{2})}$

Step 2

Pull terms out from under the radical.

$3 x^{4} y^{7} \sqrt[3]{2 y^{2}}$