Simplify x cube root of 189x^9y^11

$x \sqrt[3]{189 x^{9} y^{11}}$

Step 1

Rewrite $189 x^{9} y^{11}$ as ${(3 x^{3} y^{3})}^{3} \cdot (7 y^{2})$ .

Factor $27$ out of $189$ .

$x \sqrt[3]{27 (7) x^{9} y^{11}}$

Rewrite $27$ as $3^{3}$ .

$x \sqrt[3]{3^{3} \cdot 7 x^{9} y^{11}}$

Rewrite $x^{9}$ as ${(x^{3})}^{3}$ .

$x \sqrt[3]{3^{3} \cdot 7 {(x^{3})}^{3} y^{11}}$

Factor out $y^{9}$ .

$x \sqrt[3]{3^{3} \cdot 7 {(x^{3})}^{3} (y^{9} y^{2})}$

Rewrite $y^{9}$ as ${(y^{3})}^{3}$ .

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

Move $7$ .

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

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

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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

Step 3

Rewrite using the commutative property of multiplication.

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

Step 4

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

Move $x^{3}$ .

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

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

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

$3 (x^{3} x^{1}) (y^{3} \sqrt[3]{7 y^{2}})$

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

$3 x^{3 + 1} (y^{3} \sqrt[3]{7 y^{2}})$

Add $3$ and $1$ .

$3 x^{4} (y^{3} \sqrt[3]{7 y^{2}})$

$3 x^{4} y^{3} \sqrt[3]{7 y^{2}}$