Simplify the Radical Expression cube root of (250f^7g^3)/(2f^2g)

$\sqrt[3]{\frac{250 f^{7} g^{3}}{2 f^{2} g}}$

Step 1

Reduce the expression $\frac{250 f^{7} g^{3}}{2 f^{2} g}$ by cancelling the common factors.

Factor $2$ out of $250 f^{7} g^{3}$ .

$\sqrt[3]{\frac{2 (125 f^{7} g^{3})}{2 f^{2} g}}$

Factor $2$ out of $2 f^{2} g$ .

$\sqrt[3]{\frac{2 (125 f^{7} g^{3})}{2 (f^{2} g)}}$

Cancel the common factor.

$\sqrt[3]{\frac{2 (125 f^{7} g^{3})}{2 (f^{2} g)}}$

Rewrite the expression.

$\sqrt[3]{\frac{125 f^{7} g^{3}}{f^{2} g}}$

Step 2

Cancel the common factor of $f^{7}$ and $f^{2}$ .

Factor $f^{2}$ out of $125 f^{7} g^{3}$ .

$\sqrt[3]{\frac{f^{2} (125 f^{5} g^{3})}{f^{2} g}}$

Cancel the common factors.

Factor $f^{2}$ out of $f^{2} g$ .

$\sqrt[3]{\frac{f^{2} (125 f^{5} g^{3})}{f^{2} (g)}}$

Cancel the common factor.

$\sqrt[3]{\frac{f^{2} (125 f^{5} g^{3})}{f^{2} g}}$

Rewrite the expression.

$\sqrt[3]{\frac{125 f^{5} g^{3}}{g}}$

Step 3

Cancel the common factor of $g^{3}$ and $g$ .

Factor $g$ out of $125 f^{5} g^{3}$ .

$\sqrt[3]{\frac{g (125 f^{5} g^{2})}{g}}$

Cancel the common factors.

Raise $g$ to the power of $1$ .

$\sqrt[3]{\frac{g (125 f^{5} g^{2})}{g^{1}}}$

Factor $g$ out of $g^{1}$ .

$\sqrt[3]{\frac{g (125 f^{5} g^{2})}{g \cdot 1}}$

Cancel the common factor.

$\sqrt[3]{\frac{g (125 f^{5} g^{2})}{g \cdot 1}}$

Rewrite the expression.

$\sqrt[3]{\frac{125 f^{5} g^{2}}{1}}$

Divide $125 f^{5} g^{2}$ by $1$ .

$\sqrt[3]{125 f^{5} g^{2}}$

Step 4

Rewrite $125 f^{5} g^{2}$ as ${(5 f)}^{3} (f^{2} g^{2})$ .

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

$\sqrt[3]{5^{3} f^{5} g^{2}}$

Factor out $f^{3}$ .

$\sqrt[3]{5^{3} (f^{3} f^{2}) g^{2}}$

Rewrite $5^{3} f^{3}$ as ${(5 f)}^{3}$ .

$\sqrt[3]{{(5 f)}^{3} f^{2} g^{2}}$

Add parentheses.

$\sqrt[3]{{(5 f)}^{3} (f^{2} g^{2})}$

Step 5

Pull terms out from under the radical.

$5 f \sqrt[3]{f^{2} g^{2}}$

Simplify the Radical Expression cube root of (250f^7g^3)/(2f^2g)

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