Evaluate fourth root of (24x^6y)/(128x^4y^5)

$\sqrt[4]{\frac{24 x^{6} y}{128 x^{4} y^{5}}}$

Step 1

Reduce the expression $\frac{24 x^{6} y}{128 x^{4} y^{5}}$ by cancelling the common factors.

Factor $8$ out of $24 x^{6} y$ .

$\sqrt[4]{\frac{8 (3 x^{6} y)}{128 x^{4} y^{5}}}$

Factor $8$ out of $128 x^{4} y^{5}$ .

$\sqrt[4]{\frac{8 (3 x^{6} y)}{8 (16 x^{4} y^{5})}}$

Cancel the common factor.

$\sqrt[4]{\frac{8 (3 x^{6} y)}{8 (16 x^{4} y^{5})}}$

Rewrite the expression.

$\sqrt[4]{\frac{3 x^{6} y}{16 x^{4} y^{5}}}$

Step 2

Cancel the common factor of $x^{6}$ and $x^{4}$ .

Factor $x^{4}$ out of $3 x^{6} y$ .

$\sqrt[4]{\frac{x^{4} (3 x^{2} y)}{16 x^{4} y^{5}}}$

Cancel the common factors.

Factor $x^{4}$ out of $16 x^{4} y^{5}$ .

$\sqrt[4]{\frac{x^{4} (3 x^{2} y)}{x^{4} (16 y^{5})}}$

Cancel the common factor.

$\sqrt[4]{\frac{x^{4} (3 x^{2} y)}{x^{4} (16 y^{5})}}$

Rewrite the expression.

$\sqrt[4]{\frac{3 x^{2} y}{16 y^{5}}}$

Step 3

Cancel the common factor of $y$ and $y^{5}$ .

Factor $y$ out of $3 x^{2} y$ .

$\sqrt[4]{\frac{y (3 x^{2})}{16 y^{5}}}$

Cancel the common factors.

Factor $y$ out of $16 y^{5}$ .

$\sqrt[4]{\frac{y (3 x^{2})}{y (16 y^{4})}}$

Cancel the common factor.

$\sqrt[4]{\frac{y (3 x^{2})}{y (16 y^{4})}}$

Rewrite the expression.

$\sqrt[4]{\frac{3 x^{2}}{16 y^{4}}}$

Step 4

Rewrite $\frac{3 x^{2}}{16 y^{4}}$ as ${(\frac{1}{2 y})}^{4} (3 x^{2})$ .

Factor the perfect power $1^{4}$ out of $3 x^{2}$ .

$\sqrt[4]{\frac{1^{4} (3 x^{2})}{16 y^{4}}}$

Factor the perfect power ${(2 y)}^{4}$ out of $16 y^{4}$ .

$\sqrt[4]{\frac{1^{4} (3 x^{2})}{{(2 y)}^{4} \cdot 1}}$

Rearrange the fraction $\frac{1^{4} (3 x^{2})}{{(2 y)}^{4} \cdot 1}$ .

$\sqrt[4]{{(\frac{1}{2 y})}^{4} (3 x^{2})}$

Step 5

Pull terms out from under the radical.

$\frac{1}{2 y} \sqrt[4]{3 x^{2}}$

Step 6

Combine $\frac{1}{2 y}$ and $\sqrt[4]{3 x^{2}}$ .

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

Evaluate fourth root of (24x^6y)/(128x^4y^5)

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