Simplify cube root of 24xy^3+y cube root of 81x

$\sqrt[3]{24 x y^{3}} + y \sqrt[3]{81 x}$

Step 1

Simplify each term.

Rewrite $24 x y^{3}$ as ${(2 y)}^{3} \cdot (3 x)$ .

Factor $8$ out of $24$ .

$\sqrt[3]{8 (3) x y^{3}} + y \sqrt[3]{81 x}$

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

$\sqrt[3]{2^{3} \cdot 3 x y^{3}} + y \sqrt[3]{81 x}$

Move $x$ .

$\sqrt[3]{2^{3} \cdot 3 y^{3} x} + y \sqrt[3]{81 x}$

Move $3$ .

$\sqrt[3]{2^{3} y^{3} \cdot 3 x} + y \sqrt[3]{81 x}$

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

$\sqrt[3]{{(2 y)}^{3} \cdot 3 x} + y \sqrt[3]{81 x}$

Add parentheses.

$\sqrt[3]{{(2 y)}^{3} \cdot (3 x)} + y \sqrt[3]{81 x}$

Pull terms out from under the radical.

$2 y \sqrt[3]{3 x} + y \sqrt[3]{81 x}$

Rewrite $81 x$ as $3^{3} \cdot (3 x)$ .

Factor $27$ out of $81$ .

$2 y \sqrt[3]{3 x} + y \sqrt[3]{27 (3) x}$

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

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

Add parentheses.

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

Pull terms out from under the radical.

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

Rewrite using the commutative property of multiplication.

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

Step 2

Add $2 y \sqrt[3]{3 x}$ and $3 y \sqrt[3]{3 x}$ .

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