Simplify x square root of 54x^6y^5

$x \sqrt{54 x^{6} y^{5}}$

Step 1

Rewrite $54 x^{6} y^{5}$ as ${(3 x^{3} y^{2})}^{2} \cdot (6 y)$ .

Factor $9$ out of $54$ .

$x \sqrt{9 (6) x^{6} y^{5}}$

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

$x \sqrt{3^{2} \cdot 6 x^{6} y^{5}}$

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

$x \sqrt{3^{2} \cdot 6 {(x^{3})}^{2} y^{5}}$

Factor out $y^{4}$ .

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

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

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

Move $6$ .

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

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

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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

Step 3

Rewrite using the commutative property of multiplication.

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

Step 4

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

Move $x^{3}$ .

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

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

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

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

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

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

Add $3$ and $1$ .

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

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