Algebra Examples

$\frac{\sqrt[3]{6 y^{8}}}{\sqrt[3]{125 x^{9}}}$

Step 1

Simplify the numerator.

Tap for more steps...

Step 1.1

Rewrite $6 y^{8}$ as ${(y^{2})}^{3} \cdot (6 y^{2})$ .

Tap for more steps...

Step 1.1.1

Factor out $y^{6}$ .

$\frac{\sqrt[3]{6 (y^{6} y^{2})}}{\sqrt[3]{125 x^{9}}}$

Step 1.1.2

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

$\frac{\sqrt[3]{6 ({(y^{2})}^{3} y^{2})}}{\sqrt[3]{125 x^{9}}}$

Step 1.1.3

Reorder $6$ and ${(y^{2})}^{3}$ .

$\frac{\sqrt[3]{{(y^{2})}^{3} \cdot 6 y^{2}}}{\sqrt[3]{125 x^{9}}}$

Step 1.1.4

Add parentheses.

$\frac{\sqrt[3]{{(y^{2})}^{3} \cdot (6 y^{2})}}{\sqrt[3]{125 x^{9}}}$

Step 1.2

Pull terms out from under the radical.

$\frac{y^{2} \sqrt[3]{6 y^{2}}}{\sqrt[3]{125 x^{9}}}$

Step 2

Simplify the denominator.

Tap for more steps...

Step 2.1

Rewrite $125 x^{9}$ as ${(5 x^{3})}^{3}$ .

$\frac{y^{2} \sqrt[3]{6 y^{2}}}{\sqrt[3]{{(5 x^{3})}^{3}}}$

Step 2.2

Pull terms out from under the radical, assuming real numbers.

$\frac{y^{2} \sqrt[3]{6 y^{2}}}{5 x^{3}}$