Simplify (5x^2y)/( fourth root of x^4y^3)

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

Pull terms out from under the radical.

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

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

Factor $x$ out of $5 x^{2} y$ .

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

Cancel the common factors.

Factor $x$ out of $x \sqrt[4]{y^{3}}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $\frac{5 x y}{\sqrt[4]{y^{3}}}$ by $\frac{{\sqrt[4]{y^{3}}}^{3}}{{\sqrt[4]{y^{3}}}^{3}}$ .

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

Simplify terms.

Combine and simplify the denominator.

Multiply $\frac{5 x y}{\sqrt[4]{y^{3}}}$ by $\frac{{\sqrt[4]{y^{3}}}^{3}}{{\sqrt[4]{y^{3}}}^{3}}$ .

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

Raise $\sqrt[4]{y^{3}}$ to the power of $1$ .

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

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

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

Add $1$ and $3$ .

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

Rewrite ${\sqrt[4]{y^{3}}}^{4}$ as $y^{3}$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[4]{y^{3}}$ as $y^{\frac{3}{4}}$ .

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

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

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

Combine $\frac{3}{4}$ and $4$ .

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

Multiply $3$ by $4$ .

$\frac{5 x y {\sqrt[4]{y^{3}}}^{3}}{y^{\frac{12}{4}}}$

Cancel the common factor of $12$ and $4$ .

Factor $4$ out of $12$ .

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

Cancel the common factors.

Factor $4$ out of $4$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Divide $3$ by $1$ .

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

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

Factor $y$ out of $5 x y {\sqrt[4]{y^{3}}}^{3}$ .

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Simplify the numerator.

Rewrite ${\sqrt[4]{y^{3}}}^{3}$ as ${({(y^{3})}^{3})}^{\frac{1}{4}}$ .

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

Multiply the exponents in ${(y^{3})}^{3}$ .

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

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

Multiply $3$ by $3$ .

$\frac{5 x \sqrt[4]{y^{9}}}{y^{2}}$

Rewrite $y^{9}$ as ${(y^{2})}^{4} y$ .

Factor out $y^{8}$ .

$\frac{5 x \sqrt[4]{y^{8} y}}{y^{2}}$

Rewrite $y^{8}$ as ${(y^{2})}^{4}$ .

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

Pull terms out from under the radical.

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

Cancel the common factor of $y^{2}$ .

Cancel the common factor.

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

Divide $5 x \sqrt[4]{y}$ by $1$ .

$5 x \sqrt[4]{y}$

Simplify (5x^2y)/( fourth root of x^4y^3)

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