Basic Math Examples

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

Step 1

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

$- 1 \cdot 4 - 3 {(- 2 \cdot 3)}^{- 1}$

Step 2

Multiply $- 1$ by $4$ .

$- 4 - 3 {(- 2 \cdot 3)}^{- 1}$

Step 3

Multiply $- 2$ by $3$ .

$- 4 - 3 {(- 6)}^{- 1}$

Step 4

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$- 4 - 3 (\frac{1}{- 6})$

Step 5

Cancel the common factor of $3$ .

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Step 5.1

Factor $3$ out of $- 3$ .

$- 4 + 3 (- 1) \frac{1}{- 6}$

Step 5.2

Factor $3$ out of $- 6$ .

$- 4 + 3 \cdot - 1 \frac{1}{3 \cdot - 2}$

Step 5.3

Cancel the common factor.

$- 4 + 3 \cdot - 1 \frac{1}{3 \cdot - 2}$

Step 5.4

Rewrite the expression.

$- 4 - 1 (\frac{1}{- 2})$

Step 6

Move the negative in front of the fraction.

$- 4 - 1 (- \frac{1}{2})$

Step 7

Multiply $- 1 (- \frac{1}{2})$ .

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Step 7.1

Multiply $- 1$ by $- 1$ .

$- 4 + 1 (\frac{1}{2})$

Step 7.2

Multiply $\frac{1}{2}$ by $1$ .

$- 4 + \frac{1}{2}$

Step 8

To write $- 4$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- 4 \cdot \frac{2}{2} + \frac{1}{2}$

Step 9

Combine $- 4$ and $\frac{2}{2}$ .

$\frac{- 4 \cdot 2}{2} + \frac{1}{2}$

Step 10

Combine the numerators over the common denominator.

$\frac{- 4 \cdot 2 + 1}{2}$

Step 11

Simplify the numerator.

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Step 11.1

Multiply $- 4$ by $2$ .

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

Step 11.2

Add $- 8$ and $1$ .

$\frac{- 7}{2}$

Step 12

Move the negative in front of the fraction.

$- \frac{7}{2}$