Basic Math Examples

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

Step 1

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

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

Step 2

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

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

Step 3

Combine the numerators over the common denominator.

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

Step 4

Simplify the numerator.

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Step 4.1

Multiply $3$ by $2$ .

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

Step 4.2

Subtract $1$ from $6$ .

${(\frac{5}{2})}^{- 2}$

Step 5

Change the sign of the exponent by rewriting the base as its reciprocal.

${(\frac{2}{5})}^{2}$

Step 6

Apply the product rule to $\frac{2}{5}$ .

$\frac{2^{2}}{5^{2}}$

Step 7

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

$\frac{4}{5^{2}}$

Step 8

Raise $5$ to the power of $2$ .

$\frac{4}{25}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$\frac{4}{25}$

Decimal Form:

$0.16$