Simplify 6xy^3 square root of 36x^6y^6

$6 x y^{3} \sqrt{36 x^{6} y^{6}}$

Rewrite $36 x^{6} y^{6}$ as ${(6 x^{3} y^{3})}^{2}$ .

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

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

$6 x y^{3} (6 x^{3} y^{3})$

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

Move $x^{3}$ .

$6 (x^{3} x) y^{3} (6 y^{3})$

Multiply $x^{3}$ by $x$ .

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

$6 (x^{3} x^{1}) y^{3} (6 y^{3})$

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

$6 x^{3 + 1} y^{3} (6 y^{3})$

Add $3$ and $1$ .

$6 x^{4} y^{3} (6 y^{3})$

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

Move $y^{3}$ .

$6 x^{4} (y^{3} y^{3}) \cdot 6$

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

$6 x^{4} y^{3 + 3} \cdot 6$

Add $3$ and $3$ .

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

Multiply $6$ by $6$ .

$36 x^{4} y^{6}$