Simplify 25xy square root of 81/625x^2y^2

$25 x y \sqrt{\frac{81}{625} x^{2} y^{2}}$

Combine $\frac{81}{625}$ and $x^{2}$ .

$25 x y \sqrt{\frac{81 x^{2}}{625} y^{2}}$

Combine $\frac{81 x^{2}}{625}$ and $y^{2}$ .

$25 x y \sqrt{\frac{81 x^{2} y^{2}}{625}}$

Rewrite $81 x^{2} y^{2}$ as ${(9 x y)}^{2}$ .

$25 x y \sqrt{\frac{{(9 x y)}^{2}}{625}}$

Rewrite $625$ as $25^{2}$ .

$25 x y \sqrt{\frac{{(9 x y)}^{2}}{25^{2}}}$

Rewrite $\frac{{(9 x y)}^{2}}{25^{2}}$ as ${(\frac{9 x y}{25})}^{2}$ .

$25 x y \sqrt{{(\frac{9 x y}{25})}^{2}}$

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

$25 x y \frac{9 x y}{25}$

Cancel the common factor of $25$ .

Factor $25$ out of $25 x y$ .

$25 (x y) \frac{9 x y}{25}$

Cancel the common factor.

$25 (x y) \frac{9 x y}{25}$

Rewrite the expression.

$x y (9 x y)$

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

$x^{1} x y (9 y)$

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

$x^{1} x^{1} y (9 y)$

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

$x^{1 + 1} y (9 y)$

Add $1$ and $1$ .

$x^{2} y (9 y)$

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

$x^{2} (9 (y^{1} y))$

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

$x^{2} (9 (y^{1} y^{1}))$

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

$x^{2} (9 y^{1 + 1})$

Add $1$ and $1$ .

$x^{2} (9 y^{2})$

Rewrite using the commutative property of multiplication.

$9 x^{2} y^{2}$