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

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

Step 1

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

Factor $9$ out of $54$ .

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

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

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

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

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

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

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

Move $6$ .

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

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

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

Step 2

Pull terms out from under the radical.

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

Step 3

Rewrite using the commutative property of multiplication.

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

Step 4

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

Move $x^{3}$ .

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

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

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

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

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

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

Add $3$ and $1$ .

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