Pre-Algebra Examples

$\sqrt[3]{256 x^{10} y^{7}}$

Step 1

Rewrite $256 x^{10} y^{7}$ as ${(4 x^{3} y^{2})}^{3} \cdot (4 x y)$ .

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Step 1.1

Factor $64$ out of $256$ .

$\sqrt[3]{64 (4) x^{10} y^{7}}$

Step 1.2

Rewrite $64$ as $4^{3}$ .

$\sqrt[3]{4^{3} \cdot 4 x^{10} y^{7}}$

Step 1.3

Factor out $x^{9}$ .

$\sqrt[3]{4^{3} \cdot 4 (x^{9} x) y^{7}}$

Step 1.4

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

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

Step 1.5

Factor out $y^{6}$ .

$\sqrt[3]{4^{3} \cdot 4 ({(x^{3})}^{3} x) (y^{6} y)}$

Step 1.6

Rewrite $y^{6}$ as ${(y^{2})}^{3}$ .

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

Step 1.7

Move $x$ .

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

Step 1.8

Move $4$ .

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

Step 1.9

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

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

Step 1.10

Add parentheses.

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

Step 1.11

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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