Simplify cube root of -40a^7+2a^2* cube root of 135a^4

$\sqrt[3]{- 40 a^{7}} + 2 a^{2} \cdot \sqrt[3]{135 a^{4}}$

Rewrite $- 40 a^{7}$ as ${(- 2 a^{2})}^{3} \cdot (5 a)$ .

Factor $- 8$ out of $- 40$ .

$\sqrt[3]{- 8 (5) a^{7}} + 2 a^{2} \cdot \sqrt[3]{135 a^{4}}$

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

$\sqrt[3]{{(- 2)}^{3} \cdot 5 a^{7}} + 2 a^{2} \cdot \sqrt[3]{135 a^{4}}$

Factor out $a^{6}$ .

$\sqrt[3]{{(- 2)}^{3} \cdot 5 (a^{6} a)} + 2 a^{2} \cdot \sqrt[3]{135 a^{4}}$

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

$\sqrt[3]{{(- 2)}^{3} \cdot 5 ({(a^{2})}^{3} a)} + 2 a^{2} \cdot \sqrt[3]{135 a^{4}}$

Move $5$ .

$\sqrt[3]{{(- 2)}^{3} {(a^{2})}^{3} \cdot 5 a} + 2 a^{2} \cdot \sqrt[3]{135 a^{4}}$

Rewrite ${(- 2)}^{3} {(a^{2})}^{3}$ as ${(- 2 a^{2})}^{3}$ .

$\sqrt[3]{{(- 2 a^{2})}^{3} \cdot 5 a} + 2 a^{2} \cdot \sqrt[3]{135 a^{4}}$

Add parentheses.

$\sqrt[3]{{(- 2 a^{2})}^{3} \cdot (5 a)} + 2 a^{2} \cdot \sqrt[3]{135 a^{4}}$

Pull terms out from under the radical.

$- 2 a^{2} \sqrt[3]{5 a} + 2 a^{2} \cdot \sqrt[3]{135 a^{4}}$

Rewrite $135 a^{4}$ as ${(3 a)}^{3} \cdot (5 a)$ .

Factor $27$ out of $135$ .

$- 2 a^{2} \sqrt[3]{5 a} + 2 a^{2} \cdot \sqrt[3]{27 (5) a^{4}}$

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

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

Factor out $a^{3}$ .

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

Move $5$ .

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

Rewrite $3^{3} a^{3}$ as ${(3 a)}^{3}$ .

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

Add parentheses.

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

Pull terms out from under the radical.

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

Multiply $a^{2}$ by $a$ by adding the exponents.

Move $a$ .

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

Multiply $a$ by $a^{2}$ .

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

$- 2 a^{2} \sqrt[3]{5 a} + 2 (a^{1} a^{2}) \cdot (3 \sqrt[3]{5 a})$

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

$- 2 a^{2} \sqrt[3]{5 a} + 2 a^{1 + 2} \cdot (3 \sqrt[3]{5 a})$

Add $1$ and $2$ .

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

Multiply $3$ by $2$ .

$- 2 a^{2} \sqrt[3]{5 a} + 6 a^{3} \sqrt[3]{5 a}$