Write the Fraction in Simplest Form fourth root of (405x^3y^3)/(5x^-1y)

$\sqrt[4]{\frac{405 x^{3} y^{3}}{5 x^{- 1} y}}$

Reduce the expression $\frac{405 x^{3} y^{3}}{5 x^{- 1} y}$ by cancelling the common factors.

Factor $5$ out of $405 x^{3} y^{3}$ .

$\sqrt[4]{\frac{5 (81 x^{3} y^{3})}{5 x^{- 1} y}}$

Factor $5$ out of $5 x^{- 1} y$ .

$\sqrt[4]{\frac{5 (81 x^{3} y^{3})}{5 (x^{- 1} y)}}$

Cancel the common factor.

$\sqrt[4]{\frac{5 (81 x^{3} y^{3})}{5 (x^{- 1} y)}}$

Rewrite the expression.

$\sqrt[4]{\frac{81 x^{3} y^{3}}{x^{- 1} y}}$

Move $x^{- 1}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\sqrt[4]{\frac{81 x^{3} y^{3} x}{y}}$

Multiply $x^{3}$ by $x$ by adding the exponents.

Move $x$ .

$\sqrt[4]{\frac{81 (x \cdot x^{3}) y^{3}}{y}}$

Multiply $x$ by $x^{3}$ .

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

$\sqrt[4]{\frac{81 (x^{1} x^{3}) y^{3}}{y}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\sqrt[4]{\frac{81 x^{1 + 3} y^{3}}{y}}$

Add $1$ and $3$ .

$\sqrt[4]{\frac{81 x^{4} y^{3}}{y}}$

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

Factor $y$ out of $81 x^{4} y^{3}$ .

$\sqrt[4]{\frac{y (81 x^{4} y^{2})}{y}}$

Cancel the common factors.

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

$\sqrt[4]{\frac{y (81 x^{4} y^{2})}{y^{1}}}$

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

$\sqrt[4]{\frac{y (81 x^{4} y^{2})}{y \cdot 1}}$

Cancel the common factor.

$\sqrt[4]{\frac{y (81 x^{4} y^{2})}{y \cdot 1}}$

Rewrite the expression.

$\sqrt[4]{\frac{81 x^{4} y^{2}}{1}}$

Divide $81 x^{4} y^{2}$ by $1$ .

$\sqrt[4]{81 x^{4} y^{2}}$

Rewrite $81 x^{4} y^{2}$ as ${(3 x)}^{4} y^{2}$ .

Rewrite $81$ as $3^{4}$ .

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

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

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

Pull terms out from under the radical.

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

Rewrite $\sqrt[4]{y^{2}}$ as $\sqrt{\sqrt{y^{2}}}$ .

$3 x \sqrt{\sqrt{y^{2}}}$

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

$3 x \sqrt{y}$

Write the Fraction in Simplest Form fourth root of (405x^3y^3)/(5x^-1y)

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