Algebra Examples

$(\frac{1}{6} {(2)}^{6} + \frac{1}{3} {(2)}^{3} - (\frac{1}{6} {(0)}^{6} + \frac{1}{3} {(0)}^{3}))$

Step 1

Simplify each term.

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Step 1.1

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

$\frac{1}{6} \cdot 64 + \frac{1}{3} \cdot {(2)}^{3} - (\frac{1}{6} \cdot {(0)}^{6} + \frac{1}{3} \cdot {(0)}^{3})$

Step 1.2

Cancel the common factor of $2$ .

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Step 1.2.1

Factor $2$ out of $6$ .

$\frac{1}{2 (3)} \cdot 64 + \frac{1}{3} \cdot {(2)}^{3} - (\frac{1}{6} \cdot {(0)}^{6} + \frac{1}{3} \cdot {(0)}^{3})$

Step 1.2.2

Factor $2$ out of $64$ .

$\frac{1}{2 \cdot 3} \cdot (2 \cdot 32) + \frac{1}{3} \cdot {(2)}^{3} - (\frac{1}{6} \cdot {(0)}^{6} + \frac{1}{3} \cdot {(0)}^{3})$

Step 1.2.3

Cancel the common factor.

$\frac{1}{2 \cdot 3} \cdot (2 \cdot 32) + \frac{1}{3} \cdot {(2)}^{3} - (\frac{1}{6} \cdot {(0)}^{6} + \frac{1}{3} \cdot {(0)}^{3})$

Step 1.2.4

Rewrite the expression.

$\frac{1}{3} \cdot 32 + \frac{1}{3} \cdot {(2)}^{3} - (\frac{1}{6} \cdot {(0)}^{6} + \frac{1}{3} \cdot {(0)}^{3})$

Step 1.3

Combine $\frac{1}{3}$ and $32$ .

$\frac{32}{3} + \frac{1}{3} \cdot {(2)}^{3} - (\frac{1}{6} \cdot {(0)}^{6} + \frac{1}{3} \cdot {(0)}^{3})$

Step 1.4

Raise $2$ to the power of $3$ .

$\frac{32}{3} + \frac{1}{3} \cdot 8 - (\frac{1}{6} \cdot {(0)}^{6} + \frac{1}{3} \cdot {(0)}^{3})$

Step 1.5

Combine $\frac{1}{3}$ and $8$ .

$\frac{32}{3} + \frac{8}{3} - (\frac{1}{6} \cdot {(0)}^{6} + \frac{1}{3} \cdot {(0)}^{3})$

Step 1.6

Simplify each term.

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Step 1.6.1

Raising $0$ to any positive power yields $0$ .

$\frac{32}{3} + \frac{8}{3} - (\frac{1}{6} \cdot 0 + \frac{1}{3} \cdot {(0)}^{3})$

Step 1.6.2

Multiply $\frac{1}{6}$ by $0$ .

$\frac{32}{3} + \frac{8}{3} - (0 + \frac{1}{3} \cdot {(0)}^{3})$

Step 1.6.3

Raising $0$ to any positive power yields $0$ .

$\frac{32}{3} + \frac{8}{3} - (0 + \frac{1}{3} \cdot 0)$

Step 1.6.4

Multiply $\frac{1}{3}$ by $0$ .

$\frac{32}{3} + \frac{8}{3} - (0 + 0)$

Step 1.7

Add $0$ and $0$ .

$\frac{32}{3} + \frac{8}{3} - 0$

Step 1.8

Multiply $- 1$ by $0$ .

$\frac{32}{3} + \frac{8}{3} + 0$

Step 2

Combine fractions.

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Step 2.1

Combine the numerators over the common denominator.

$\frac{32 + 8}{3}$

Step 2.2

Add $32$ and $8$ .

$\frac{40}{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{40}{3}$

Decimal Form:

$13.\overline{3}$

Mixed Number Form:

$13 \frac{1}{3}$