Simplify x^3y^3 cube root of 648x^3y^10

$x^{3} y^{3} \sqrt[3]{648 x^{3} y^{10}}$

Step 1

Rewrite $648 x^{3} y^{10}$ as ${(6 x y^{3})}^{3} \cdot (3 y)$ .

Factor $216$ out of $648$ .

$x^{3} y^{3} \sqrt[3]{216 (3) x^{3} y^{10}}$

Rewrite $216$ as $6^{3}$ .

$x^{3} y^{3} \sqrt[3]{6^{3} \cdot 3 x^{3} y^{10}}$

Factor out $y^{9}$ .

$x^{3} y^{3} \sqrt[3]{6^{3} \cdot 3 x^{3} (y^{9} y)}$

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

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

Move $3$ .

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

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

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

Add parentheses.

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

Step 2

Pull terms out from under the radical.

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

Step 3

Rewrite using the commutative property of multiplication.

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

Step 4

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

Move $x$ .

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

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

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

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

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

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

Add $1$ and $3$ .

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

Step 5

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

Move $y^{3}$ .

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

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

$6 x^{4} y^{3 + 3} \sqrt[3]{3 y}$

Add $3$ and $3$ .

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