Simplify x square root of 54x^4y^6

$x \sqrt{54 x^{4} y^{6}}$

Rewrite $54 x^{4} y^{6}$ as ${(3 x^{2} y^{3})}^{2} \cdot 6$ .

Factor $9$ out of $54$ .

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

Rewrite $9$ as $3^{2}$ .

$x \sqrt{3^{2} \cdot 6 x^{4} y^{6}}$

Rewrite $x^{4}$ as ${(x^{2})}^{2}$ .

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

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

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

Move $6$ .

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

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

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

Pull terms out from under the radical.

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

Rewrite using the commutative property of multiplication.

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

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

Move $x^{2}$ .

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

Multiply $x^{2}$ by $x$ .

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

$3 \sqrt{6} (x^{2} x^{1}) y^{3}$

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

$3 \sqrt{6} x^{2 + 1} y^{3}$

Add $2$ and $1$ .

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