Basic Math Examples

${(- \frac{12}{5})}^{- 2}$

Step 1

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

${(- \frac{5}{12})}^{2}$

Step 2

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 2.1

Apply the product rule to $- \frac{5}{12}$ .

${(- 1)}^{2} {(\frac{5}{12})}^{2}$

Step 2.2

Apply the product rule to $\frac{5}{12}$ .

${(- 1)}^{2} \frac{5^{2}}{12^{2}}$

Step 3

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

$1 \frac{5^{2}}{12^{2}}$

Step 4

Multiply $\frac{5^{2}}{12^{2}}$ by $1$ .

$\frac{5^{2}}{12^{2}}$

Step 5

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

$\frac{25}{12^{2}}$

Step 6

Raise $12$ to the power of $2$ .

$\frac{25}{144}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{25}{144}$

Decimal Form:

$0.1736\overline{1}$