Simplify (2x^-4y^(1/4))/( square root of 25x^4y)

$\frac{2 x^{- 4} y^{\frac{1}{4}}}{\sqrt{25 x^{4} y}}$

Move $x^{- 4}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{2 y^{\frac{1}{4}}}{\sqrt{25 x^{4} y} x^{4}}$

Simplify the denominator.

Rewrite $25 x^{4} y$ as ${(5 x^{2})}^{2} y$ .

Rewrite $25$ as $5^{2}$ .

$\frac{2 y^{\frac{1}{4}}}{\sqrt{5^{2} x^{4} y} x^{4}}$

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

$\frac{2 y^{\frac{1}{4}}}{\sqrt{5^{2} {(x^{2})}^{2} y} x^{4}}$

Rewrite $5^{2} {(x^{2})}^{2}$ as ${(5 x^{2})}^{2}$ .

$\frac{2 y^{\frac{1}{4}}}{\sqrt{{(5 x^{2})}^{2} y} x^{4}}$

Pull terms out from under the radical.

$\frac{2 y^{\frac{1}{4}}}{5 x^{2} \sqrt{y} x^{4}}$

Multiply $x^{2}$ by $x^{4}$ by adding the exponents.

Move $x^{4}$ .

$\frac{2 y^{\frac{1}{4}}}{5 (x^{4} x^{2}) \sqrt{y}}$

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

$\frac{2 y^{\frac{1}{4}}}{5 x^{4 + 2} \sqrt{y}}$

Add $4$ and $2$ .

$\frac{2 y^{\frac{1}{4}}}{5 x^{6} \sqrt{y}}$

Multiply $\frac{2 y^{\frac{1}{4}}}{5 x^{6} \sqrt{y}}$ by $\frac{\sqrt{y}}{\sqrt{y}}$ .

$\frac{2 y^{\frac{1}{4}}}{5 x^{6} \sqrt{y}} \cdot \frac{\sqrt{y}}{\sqrt{y}}$

Combine and simplify the denominator.

Multiply $\frac{2 y^{\frac{1}{4}}}{5 x^{6} \sqrt{y}}$ by $\frac{\sqrt{y}}{\sqrt{y}}$ .

$\frac{2 y^{\frac{1}{4}} \sqrt{y}}{5 x^{6} \sqrt{y} \sqrt{y}}$

Move $\sqrt{y}$ .

$\frac{2 y^{\frac{1}{4}} \sqrt{y}}{5 x^{6} (\sqrt{y} \sqrt{y})}$

Raise $\sqrt{y}$ to the power of $1$ .

$\frac{2 y^{\frac{1}{4}} \sqrt{y}}{5 x^{6} ({\sqrt{y}}^{1} \sqrt{y})}$

Raise $\sqrt{y}$ to the power of $1$ .

$\frac{2 y^{\frac{1}{4}} \sqrt{y}}{5 x^{6} ({\sqrt{y}}^{1} {\sqrt{y}}^{1})}$

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

$\frac{2 y^{\frac{1}{4}} \sqrt{y}}{5 x^{6} {\sqrt{y}}^{1 + 1}}$

Add $1$ and $1$ .

$\frac{2 y^{\frac{1}{4}} \sqrt{y}}{5 x^{6} {\sqrt{y}}^{2}}$

Rewrite ${\sqrt{y}}^{2}$ as $y$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{y}$ as $y^{\frac{1}{2}}$ .

$\frac{2 y^{\frac{1}{4}} \sqrt{y}}{5 x^{6} {(y^{\frac{1}{2}})}^{2}}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{2 y^{\frac{1}{4}} \sqrt{y}}{5 x^{6} y^{\frac{1}{2} \cdot 2}}$

Combine $\frac{1}{2}$ and $2$ .

$\frac{2 y^{\frac{1}{4}} \sqrt{y}}{5 x^{6} y^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 y^{\frac{1}{4}} \sqrt{y}}{5 x^{6} y^{\frac{2}{2}}}$

Rewrite the expression.

$\frac{2 y^{\frac{1}{4}} \sqrt{y}}{5 x^{6} y^{1}}$

Simplify.

$\frac{2 y^{\frac{1}{4}} \sqrt{y}}{5 x^{6} y}$

Move $y^{\frac{1}{4}}$ to the denominator using the negative exponent rule $b^{n} = \frac{1}{b^{- n}}$ .

$\frac{2 \sqrt{y}}{5 x^{6} y \cdot y^{- \frac{1}{4}}}$

Multiply $y$ by $y^{- \frac{1}{4}}$ by adding the exponents.

Move $y^{- \frac{1}{4}}$ .

$\frac{2 \sqrt{y}}{5 x^{6} (y^{- \frac{1}{4}} y)}$

Multiply $y^{- \frac{1}{4}}$ by $y$ .

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

$\frac{2 \sqrt{y}}{5 x^{6} (y^{- \frac{1}{4}} y^{1})}$

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

$\frac{2 \sqrt{y}}{5 x^{6} y^{- \frac{1}{4} + 1}}$

Write $1$ as a fraction with a common denominator.

$\frac{2 \sqrt{y}}{5 x^{6} y^{- \frac{1}{4} + \frac{4}{4}}}$

Combine the numerators over the common denominator.

$\frac{2 \sqrt{y}}{5 x^{6} y^{\frac{- 1 + 4}{4}}}$

Add $- 1$ and $4$ .

$\frac{2 \sqrt{y}}{5 x^{6} y^{\frac{3}{4}}}$

Simplify (2x^-4y^(1/4))/( square root of 25x^4y)

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