Simplify 8x fourth root of 24x^4y+3x fourth root of 24x^4y-5y cube root of 12x^2y^4-4y cube root of 12x^2y^4

$8 x \sqrt[4]{24 x^{4} y} + 3 x \sqrt[4]{24 x^{4} y} - 5 y \sqrt[3]{12 x^{2} y^{4}} - 4 y \sqrt[3]{12 x^{2} y^{4}}$

Step 1

Simplify each term.

Rewrite $24 x^{4} y$ as $x^{4} \cdot (24 y)$ .

Reorder $24$ and $x^{4}$ .

$8 x \sqrt[4]{x^{4} \cdot 24 y} + 3 x \sqrt[4]{24 x^{4} y} - 5 y \sqrt[3]{12 x^{2} y^{4}} - 4 y \sqrt[3]{12 x^{2} y^{4}}$

Add parentheses.

$8 x \sqrt[4]{x^{4} \cdot (24 y)} + 3 x \sqrt[4]{24 x^{4} y} - 5 y \sqrt[3]{12 x^{2} y^{4}} - 4 y \sqrt[3]{12 x^{2} y^{4}}$

Pull terms out from under the radical.

$8 x (x \sqrt[4]{24 y}) + 3 x \sqrt[4]{24 x^{4} y} - 5 y \sqrt[3]{12 x^{2} y^{4}} - 4 y \sqrt[3]{12 x^{2} y^{4}}$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$8 (x \cdot x) \sqrt[4]{24 y} + 3 x \sqrt[4]{24 x^{4} y} - 5 y \sqrt[3]{12 x^{2} y^{4}} - 4 y \sqrt[3]{12 x^{2} y^{4}}$

Multiply $x$ by $x$ .

$8 x^{2} \sqrt[4]{24 y} + 3 x \sqrt[4]{24 x^{4} y} - 5 y \sqrt[3]{12 x^{2} y^{4}} - 4 y \sqrt[3]{12 x^{2} y^{4}}$

Rewrite $24 x^{4} y$ as $x^{4} \cdot (24 y)$ .

Reorder $24$ and $x^{4}$ .

$8 x^{2} \sqrt[4]{24 y} + 3 x \sqrt[4]{x^{4} \cdot 24 y} - 5 y \sqrt[3]{12 x^{2} y^{4}} - 4 y \sqrt[3]{12 x^{2} y^{4}}$

Add parentheses.

$8 x^{2} \sqrt[4]{24 y} + 3 x \sqrt[4]{x^{4} \cdot (24 y)} - 5 y \sqrt[3]{12 x^{2} y^{4}} - 4 y \sqrt[3]{12 x^{2} y^{4}}$

Pull terms out from under the radical.

$8 x^{2} \sqrt[4]{24 y} + 3 x (x \sqrt[4]{24 y}) - 5 y \sqrt[3]{12 x^{2} y^{4}} - 4 y \sqrt[3]{12 x^{2} y^{4}}$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$8 x^{2} \sqrt[4]{24 y} + 3 (x \cdot x) \sqrt[4]{24 y} - 5 y \sqrt[3]{12 x^{2} y^{4}} - 4 y \sqrt[3]{12 x^{2} y^{4}}$

Multiply $x$ by $x$ .

$8 x^{2} \sqrt[4]{24 y} + 3 x^{2} \sqrt[4]{24 y} - 5 y \sqrt[3]{12 x^{2} y^{4}} - 4 y \sqrt[3]{12 x^{2} y^{4}}$

Rewrite $12 x^{2} y^{4}$ as $y^{3} \cdot (12 x^{2} y)$ .

Factor out $y^{3}$ .

$8 x^{2} \sqrt[4]{24 y} + 3 x^{2} \sqrt[4]{24 y} - 5 y \sqrt[3]{12 x^{2} (y^{3} y)} - 4 y \sqrt[3]{12 x^{2} y^{4}}$

Move $x^{2}$ .

$8 x^{2} \sqrt[4]{24 y} + 3 x^{2} \sqrt[4]{24 y} - 5 y \sqrt[3]{12 y^{3} x^{2} y} - 4 y \sqrt[3]{12 x^{2} y^{4}}$

Reorder $12$ and $y^{3}$ .

$8 x^{2} \sqrt[4]{24 y} + 3 x^{2} \sqrt[4]{24 y} - 5 y \sqrt[3]{y^{3} \cdot 12 x^{2} y} - 4 y \sqrt[3]{12 x^{2} y^{4}}$

Add parentheses.

$8 x^{2} \sqrt[4]{24 y} + 3 x^{2} \sqrt[4]{24 y} - 5 y \sqrt[3]{y^{3} \cdot 12 (x^{2} y)} - 4 y \sqrt[3]{12 x^{2} y^{4}}$

Add parentheses.

$8 x^{2} \sqrt[4]{24 y} + 3 x^{2} \sqrt[4]{24 y} - 5 y \sqrt[3]{y^{3} \cdot (12 x^{2} y)} - 4 y \sqrt[3]{12 x^{2} y^{4}}$

Pull terms out from under the radical.

$8 x^{2} \sqrt[4]{24 y} + 3 x^{2} \sqrt[4]{24 y} - 5 y (y \sqrt[3]{12 x^{2} y}) - 4 y \sqrt[3]{12 x^{2} y^{4}}$

Multiply $y$ by $y$ by adding the exponents.

Move $y$ .

$8 x^{2} \sqrt[4]{24 y} + 3 x^{2} \sqrt[4]{24 y} - 5 (y \cdot y) \sqrt[3]{12 x^{2} y} - 4 y \sqrt[3]{12 x^{2} y^{4}}$

Multiply $y$ by $y$ .

$8 x^{2} \sqrt[4]{24 y} + 3 x^{2} \sqrt[4]{24 y} - 5 y^{2} \sqrt[3]{12 x^{2} y} - 4 y \sqrt[3]{12 x^{2} y^{4}}$

Rewrite $12 x^{2} y^{4}$ as $y^{3} \cdot (12 x^{2} y)$ .

Factor out $y^{3}$ .

$8 x^{2} \sqrt[4]{24 y} + 3 x^{2} \sqrt[4]{24 y} - 5 y^{2} \sqrt[3]{12 x^{2} y} - 4 y \sqrt[3]{12 x^{2} (y^{3} y)}$

Move $x^{2}$ .

$8 x^{2} \sqrt[4]{24 y} + 3 x^{2} \sqrt[4]{24 y} - 5 y^{2} \sqrt[3]{12 x^{2} y} - 4 y \sqrt[3]{12 y^{3} x^{2} y}$

Reorder $12$ and $y^{3}$ .

$8 x^{2} \sqrt[4]{24 y} + 3 x^{2} \sqrt[4]{24 y} - 5 y^{2} \sqrt[3]{12 x^{2} y} - 4 y \sqrt[3]{y^{3} \cdot 12 x^{2} y}$

Add parentheses.

$8 x^{2} \sqrt[4]{24 y} + 3 x^{2} \sqrt[4]{24 y} - 5 y^{2} \sqrt[3]{12 x^{2} y} - 4 y \sqrt[3]{y^{3} \cdot 12 (x^{2} y)}$

Add parentheses.

$8 x^{2} \sqrt[4]{24 y} + 3 x^{2} \sqrt[4]{24 y} - 5 y^{2} \sqrt[3]{12 x^{2} y} - 4 y \sqrt[3]{y^{3} \cdot (12 x^{2} y)}$

Pull terms out from under the radical.

$8 x^{2} \sqrt[4]{24 y} + 3 x^{2} \sqrt[4]{24 y} - 5 y^{2} \sqrt[3]{12 x^{2} y} - 4 y (y \sqrt[3]{12 x^{2} y})$

Multiply $y$ by $y$ by adding the exponents.

Move $y$ .

$8 x^{2} \sqrt[4]{24 y} + 3 x^{2} \sqrt[4]{24 y} - 5 y^{2} \sqrt[3]{12 x^{2} y} - 4 (y \cdot y) \sqrt[3]{12 x^{2} y}$

Multiply $y$ by $y$ .

$8 x^{2} \sqrt[4]{24 y} + 3 x^{2} \sqrt[4]{24 y} - 5 y^{2} \sqrt[3]{12 x^{2} y} - 4 y^{2} \sqrt[3]{12 x^{2} y}$

Step 2

Simplify by adding terms.

Add $8 x^{2} \sqrt[4]{24 y}$ and $3 x^{2} \sqrt[4]{24 y}$ .

$11 x^{2} \sqrt[4]{24 y} - 5 y^{2} \sqrt[3]{12 x^{2} y} - 4 y^{2} \sqrt[3]{12 x^{2} y}$

Subtract $4 y^{2} \sqrt[3]{12 x^{2} y}$ from $- 5 y^{2} \sqrt[3]{12 x^{2} y}$ .

$11 x^{2} \sqrt[4]{24 y} - 9 y^{2} \sqrt[3]{12 x^{2} y}$

Simplify 8x fourth root of 24x^4y+3x fourth root of 24x^4y-5y cube root of 12x^2y^4-4y cube root of 12x^2y^4

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