Algebra Examples

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

Step 1

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

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

Step 2

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

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

Step 3

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

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

Step 4

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

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

Step 5

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

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

Step 6

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

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

Step 7

Cancel the common factor of $25$ .

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Step 7.1

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

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

Step 7.2

Cancel the common factor.

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

Step 7.3

Rewrite the expression.

$x y (9 x y)$

Step 8

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

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

Step 9

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

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

Step 10

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

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

Step 11

Add $1$ and $1$ .

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

Step 12

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

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

Step 13

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

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

Step 14

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

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

Step 15

Add $1$ and $1$ .

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

Step 16

Rewrite using the commutative property of multiplication.

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