Simplify 3x cube root of 8x^9y^7

$3 x \sqrt[3]{8 x^{9} y^{7}}$

Step 1

Rewrite $8 x^{9} y^{7}$ as ${(2 x^{3} y^{2})}^{3} y$ .

Rewrite $8$ as $2^{3}$ .

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

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

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

Factor out $y^{6}$ .

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

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

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

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

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

Step 2

Pull terms out from under the radical.

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

Step 3

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

Move $x^{3}$ .

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

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

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

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

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

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

Add $3$ and $1$ .

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

Step 4

Multiply $2$ by $3$ .

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