Linear Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

Multiply the exponents in ${({(- 2)}^{3})}^{2}$ .

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Step 1.1.1

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

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

Step 1.1.2

Multiply $3$ by $2$ .

${(- 2)}^{6} + \sqrt[3]{- 8}$

Step 1.2

Raise $- 2$ to the power of $6$ .

$64 + \sqrt[3]{- 8}$

Step 1.3

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

$64 + \sqrt[3]{{(- 2)}^{3}}$

Step 1.4

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

$64 - 2$

Step 2

Subtract $2$ from $64$ .

$62$