Algebra Examples

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

Step 1

Apply the product rule to $- 2 a$ .

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

Step 2

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

$\sqrt[3]{16 a^{4}}$

Step 3

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

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Step 3.1

Factor $8$ out of $16$ .

$\sqrt[3]{8 (2) a^{4}}$

Step 3.2

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

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

Step 3.3

Factor out $a^{3}$ .

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

Step 3.4

Move $2$ .

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

Step 3.5

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

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

Step 3.6

Add parentheses.

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

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

Step 4

Pull terms out from under the radical.

$2 a \sqrt[3]{2 a}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$