Simplify cube root of -2^10

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

Step 1

Raise $2$ to the power of $10$ .

$\sqrt[3]{- 1 \cdot 1024}$

Step 2

Multiply $- 1$ by $1024$ .

$\sqrt[3]{- 1024}$

Step 3

Rewrite $- 1024$ as ${(- 8)}^{3} \cdot 2$ .

Factor $- 512$ out of $- 1024$ .

$\sqrt[3]{- 512 (2)}$

Rewrite $- 512$ as ${(- 8)}^{3}$ .

$\sqrt[3]{{(- 8)}^{3} \cdot 2}$

$\sqrt[3]{{(- 8)}^{3} \cdot 2}$

Step 4

Pull terms out from under the radical.

$- 8 \sqrt[3]{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- 8 \sqrt[3]{2}$

Decimal Form:

$- 10.07936839 \dots$

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