Basic Math Examples

$\frac{2^{3}}{3} - \frac{2 {(2)}^{2}}{2}$

Step 1

Simplify each term.

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Step 1.1

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

$\frac{8}{3} - \frac{2 {(2)}^{2}}{2}$

Step 1.2

Multiply $2$ by ${(2)}^{2}$ by adding the exponents.

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Step 1.2.1

Multiply $2$ by ${(2)}^{2}$ .

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Step 1.2.1.1

Raise $2$ to the power of $1$ .

$\frac{8}{3} - \frac{2^{1} {(2)}^{2}}{2}$

Step 1.2.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{8}{3} - \frac{2^{1 + 2}}{2}$

Step 1.2.2

Add $1$ and $2$ .

$\frac{8}{3} - \frac{2^{3}}{2}$

Step 1.3

Cancel the common factor of $2^{3}$ and $2$ .

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Step 1.3.1

Factor $2$ out of $2^{3}$ .

$\frac{8}{3} - \frac{2 \cdot 2^{2}}{2}$

Step 1.3.2

Cancel the common factors.

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Step 1.3.2.1

Factor $2$ out of $2$ .

$\frac{8}{3} - \frac{2 \cdot 2^{2}}{2 (1)}$

Step 1.3.2.2

Cancel the common factor.

$\frac{8}{3} - \frac{2 \cdot 2^{2}}{2 \cdot 1}$

Step 1.3.2.3

Rewrite the expression.

$\frac{8}{3} - \frac{2^{2}}{1}$

Step 1.3.2.4

Divide $2^{2}$ by $1$ .

$\frac{8}{3} - 2^{2}$

Step 1.4

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

$\frac{8}{3} - 1 \cdot 4$

Step 1.5

Multiply $- 1$ by $4$ .

$\frac{8}{3} - 4$

Step 2

To write $- 4$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{8}{3} - 4 \cdot \frac{3}{3}$

Step 3

Combine $- 4$ and $\frac{3}{3}$ .

$\frac{8}{3} + \frac{- 4 \cdot 3}{3}$

Step 4

Combine the numerators over the common denominator.

$\frac{8 - 4 \cdot 3}{3}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $- 4$ by $3$ .

$\frac{8 - 12}{3}$

Step 5.2

Subtract $12$ from $8$ .

$\frac{- 4}{3}$

Step 6

Move the negative in front of the fraction.

$- \frac{4}{3}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{4}{3}$

Decimal Form:

$- 1.\overline{3}$

Mixed Number Form:

$- 1 \frac{1}{3}$