Simplify the Radical Expression x^3 cube root of 250x^6y^6

$x^{3} \sqrt[3]{250 x^{6} y^{6}}$

Step 1

Rewrite $250 x^{6} y^{6}$ as ${(5 x^{2} y^{2})}^{3} \cdot 2$ .

Factor $125$ out of $250$ .

$x^{3} \sqrt[3]{125 (2) x^{6} y^{6}}$

Rewrite $125$ as $5^{3}$ .

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

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

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

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

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

Move $2$ .

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

Rewrite $5^{3} {(x^{2})}^{3} {(y^{2})}^{3}$ as ${(5 x^{2} y^{2})}^{3}$ .

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

Step 2

Pull terms out from under the radical.

$x^{3} (5 x^{2} y^{2} \sqrt[3]{2})$

Step 3

Rewrite using the commutative property of multiplication.

$5 \sqrt[3]{2} x^{3} (x^{2} y^{2})$

Step 4

Multiply $x^{3}$ by $x^{2}$ by adding the exponents.

Move $x^{2}$ .

$5 \sqrt[3]{2} (x^{2} x^{3}) y^{2}$

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

$5 \sqrt[3]{2} x^{2 + 3} y^{2}$

Add $2$ and $3$ .

$5 \sqrt[3]{2} x^{5} y^{2}$