Simplify cube root of 4x^2( cube root of 2x-5 cube root of 4x^2)

$\sqrt[3]{4 x^{2}} (\sqrt[3]{2 x} - 5 \sqrt[3]{4 x^{2}})$

Apply the distributive property.

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

Multiply $\sqrt[3]{4 x^{2}} \sqrt[3]{2 x}$ .

Combine using the product rule for radicals.

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

Multiply $2$ by $4$ .

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

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

$\sqrt[3]{8 (x^{1} x^{2})} + \sqrt[3]{4 x^{2}} (- 5 \sqrt[3]{4 x^{2}})$

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

$\sqrt[3]{8 x^{1 + 2}} + \sqrt[3]{4 x^{2}} (- 5 \sqrt[3]{4 x^{2}})$

Add $1$ and $2$ .

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

Rewrite using the commutative property of multiplication.

$\sqrt[3]{8 x^{3}} - 5 \sqrt[3]{4 x^{2}} \sqrt[3]{4 x^{2}}$

Simplify each term.

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

$\sqrt[3]{{(2 x)}^{3}} - 5 \sqrt[3]{4 x^{2}} \sqrt[3]{4 x^{2}}$

Pull terms out from under the radical, assuming real numbers.

$2 x - 5 \sqrt[3]{4 x^{2}} \sqrt[3]{4 x^{2}}$

Multiply $- 5 \sqrt[3]{4 x^{2}} \sqrt[3]{4 x^{2}}$ .

Raise $\sqrt[3]{4 x^{2}}$ to the power of $1$ .

$2 x - 5 ({\sqrt[3]{4 x^{2}}}^{1} \sqrt[3]{4 x^{2}})$

Raise $\sqrt[3]{4 x^{2}}$ to the power of $1$ .

$2 x - 5 ({\sqrt[3]{4 x^{2}}}^{1} {\sqrt[3]{4 x^{2}}}^{1})$

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

$2 x - 5 {\sqrt[3]{4 x^{2}}}^{1 + 1}$

Add $1$ and $1$ .

$2 x - 5 {\sqrt[3]{4 x^{2}}}^{2}$

Rewrite ${\sqrt[3]{4 x^{2}}}^{2}$ as ${({(4 x^{2})}^{2})}^{\frac{1}{3}}$ .

$2 x - 5 \sqrt[3]{{(4 x^{2})}^{2}}$

Apply the product rule to $4 x^{2}$ .

$2 x - 5 \sqrt[3]{4^{2} {(x^{2})}^{2}}$

Raise $4$ to the power of $2$ .

$2 x - 5 \sqrt[3]{16 {(x^{2})}^{2}}$

Multiply the exponents in ${(x^{2})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$2 x - 5 \sqrt[3]{16 x^{2 \cdot 2}}$

Multiply $2$ by $2$ .

$2 x - 5 \sqrt[3]{16 x^{4}}$

Rewrite $16 x^{4}$ as ${(2 x)}^{3} \cdot (2 x)$ .

Factor $8$ out of $16$ .

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

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

$2 x - 5 \sqrt[3]{2^{3} \cdot 2 x^{4}}$

Factor out $x^{3}$ .

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

Move $2$ .

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

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

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

Add parentheses.

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

Pull terms out from under the radical.

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

Multiply $2$ by $- 5$ .

$2 x - 10 x \sqrt[3]{2 x}$

Simplify cube root of 4x^2( cube root of 2x-5 cube root of 4x^2)

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