Multiply (81x^9)/(y^4)*(x^2)/(36x^5y)

$\frac{81 x^{9}}{y^{4}} \cdot \frac{x^{2}}{36 x^{5} y}$

Cancel the common factor of $9 x^{5}$ .

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Factor $9 x^{5}$ out of $81 x^{9}$ .

$\frac{9 x^{5} (9 x^{4})}{y^{4}} \cdot \frac{x^{2}}{36 x^{5} y}$

Factor $9 x^{5}$ out of $36 x^{5} y$ .

$\frac{9 x^{5} (9 x^{4})}{y^{4}} \cdot \frac{x^{2}}{9 x^{5} (4 y)}$

Cancel the common factor.

$\frac{9 x^{5} (9 x^{4})}{y^{4}} \cdot \frac{x^{2}}{9 x^{5} (4 y)}$

Rewrite the expression.

$\frac{9 x^{4}}{y^{4}} \cdot \frac{x^{2}}{4 y}$

Multiply $\frac{9 x^{4}}{y^{4}}$ and $\frac{x^{2}}{4 y}$ .

$\frac{9 x^{4} x^{2}}{y^{4} (4 y)}$

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

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Move $x^{2}$ .

$\frac{9 (x^{2} x^{4})}{y^{4} (4 y)}$

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

$\frac{9 x^{2 + 4}}{y^{4} (4 y)}$

Add $2$ and $4$ .

$\frac{9 x^{6}}{y^{4} (4 y)}$

Multiply $y^{4}$ by $y$ by adding the exponents.

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Move $y$ .

$\frac{9 x^{6}}{y \cdot y^{4} \cdot 4}$

Multiply $y$ by $y^{4}$ .

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

$\frac{9 x^{6}}{y^{1} y^{4} \cdot 4}$

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

$\frac{9 x^{6}}{y^{1 + 4} \cdot 4}$

Add $1$ and $4$ .

$\frac{9 x^{6}}{y^{5} \cdot 4}$

Move $4$ to the left of $y^{5}$ .

$\frac{9 x^{6}}{4 y^{5}}$

Multiply (81x^9)/(y^4)*(x^2)/(36x^5y)