Simplify x^2y^2 square root of 28x^6y^6

$x^{2} y^{2} \sqrt{28 x^{6} y^{6}}$

Rewrite $28 x^{6} y^{6}$ as ${(2 x^{3} y^{3})}^{2} \cdot 7$ .

Factor $4$ out of $28$ .

$x^{2} y^{2} \sqrt{4 (7) x^{6} y^{6}}$

Rewrite $4$ as $2^{2}$ .

$x^{2} y^{2} \sqrt{2^{2} \cdot 7 x^{6} y^{6}}$

Rewrite $x^{6}$ as ${(x^{3})}^{2}$ .

$x^{2} y^{2} \sqrt{2^{2} \cdot 7 {(x^{3})}^{2} y^{6}}$

Rewrite $y^{6}$ as ${(y^{3})}^{2}$ .

$x^{2} y^{2} \sqrt{2^{2} \cdot 7 {(x^{3})}^{2} {(y^{3})}^{2}}$

Move $7$ .

$x^{2} y^{2} \sqrt{2^{2} {(x^{3})}^{2} {(y^{3})}^{2} \cdot 7}$

Rewrite $2^{2} {(x^{3})}^{2} {(y^{3})}^{2}$ as ${(2 x^{3} y^{3})}^{2}$ .

$x^{2} y^{2} \sqrt{{(2 x^{3} y^{3})}^{2} \cdot 7}$

Pull terms out from under the radical.

$x^{2} y^{2} (2 x^{3} y^{3} \sqrt{7})$

Rewrite using the commutative property of multiplication.

$2 \sqrt{7} x^{2} y^{2} (x^{3} y^{3})$

Multiply $x^{2}$ by $x^{3}$ by adding the exponents.

Move $x^{3}$ .

$2 \sqrt{7} (x^{3} x^{2}) y^{2} y^{3}$

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

$2 \sqrt{7} x^{3 + 2} y^{2} y^{3}$

Add $3$ and $2$ .

$2 \sqrt{7} x^{5} y^{2} y^{3}$

Multiply $y^{2}$ by $y^{3}$ by adding the exponents.

Move $y^{3}$ .

$2 \sqrt{7} x^{5} (y^{3} y^{2})$

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

$2 \sqrt{7} x^{5} y^{3 + 2}$

Add $3$ and $2$ .

$2 \sqrt{7} x^{5} y^{5}$