Algebra Examples

${(- \sqrt[3]{- 18})}^{2}$

Step 1

Rewrite $- 18$ as ${(- 1)}^{3} \cdot 18$ .

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Step 1.1

Rewrite $- 18$ as $- 1 (18)$ .

${(- \sqrt[3]{- 1 (18)})}^{2}$

Step 1.2

Rewrite $- 1$ as ${(- 1)}^{3}$ .

${(- \sqrt[3]{{(- 1)}^{3} \cdot 18})}^{2}$

${(- \sqrt[3]{{(- 1)}^{3} \cdot 18})}^{2}$

Step 2

Pull terms out from under the radical.

${(- (- 1 \sqrt[3]{18}))}^{2}$

Step 3

Rewrite $- 1 \sqrt[3]{18}$ as $- \sqrt[3]{18}$ .

${(- - \sqrt[3]{18})}^{2}$

Step 4

Multiply $- - \sqrt[3]{18}$ .

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Step 4.1

Multiply $- 1$ by $- 1$ .

${(1 \sqrt[3]{18})}^{2}$

Step 4.2

Multiply $\sqrt[3]{18}$ by $1$ .

${\sqrt[3]{18}}^{2}$

${\sqrt[3]{18}}^{2}$

Step 5

Rewrite ${\sqrt[3]{18}}^{2}$ as $\sqrt[3]{18^{2}}$ .

$\sqrt[3]{18^{2}}$

Step 6

Raise $18$ to the power of $2$ .

$\sqrt[3]{324}$

Step 7

Rewrite $324$ as $3^{3} \cdot 12$ .

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Step 7.1

Factor $27$ out of $324$ .

$\sqrt[3]{27 (12)}$

Step 7.2

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

$\sqrt[3]{3^{3} \cdot 12}$

$\sqrt[3]{3^{3} \cdot 12}$

Step 8

Pull terms out from under the radical.

$3 \sqrt[3]{12}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$3 \sqrt[3]{12}$

Decimal Form:

$6.86828545 \dots$

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