Basic Math Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

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

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

Step 1.1.2

Cancel the common factors.

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Step 1.1.2.1

Factor $2$ out of $2$ .

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

Step 1.1.2.2

Cancel the common factor.

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

Step 1.1.2.3

Rewrite the expression.

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

Step 1.1.2.4

Divide $2$ by $1$ .

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

Step 1.2

Multiply $- 1$ by $2$ .

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

Step 1.3

Simplify the numerator.

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Step 1.3.1

Multiply $- 2$ by $2$ .

$- 2 - \frac{{(8 - 4)}^{\frac{3}{2}}}{3}$

Step 1.3.2

Subtract $4$ from $8$ .

$- 2 - \frac{4^{\frac{3}{2}}}{3}$

Step 1.3.3

Rewrite $4$ as $2^{2}$ .

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

Step 1.3.4

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

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

Step 1.3.5

Cancel the common factor of $2$ .

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Step 1.3.5.1

Cancel the common factor.

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

Step 1.3.5.2

Rewrite the expression.

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

Step 1.3.6

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

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

Step 2

To write $- 2$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 3

Combine $- 2$ and $\frac{3}{3}$ .

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

Step 4

Combine the numerators over the common denominator.

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

Step 5

Simplify the numerator.

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Step 5.1

Multiply $- 2$ by $3$ .

$\frac{- 6 - 8}{3}$

Step 5.2

Subtract $8$ from $- 6$ .

$\frac{- 14}{3}$

Step 6

Move the negative in front of the fraction.

$- \frac{14}{3}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{14}{3}$

Decimal Form:

$- 4.\overline{6}$

Mixed Number Form:

$- 4 \frac{2}{3}$