Evaluate -2(2/5)^-2

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

Step 1

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

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

Step 2

Simplify the expression.

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

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

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

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

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

$- 2 (\frac{25}{4})$

Step 3

Cancel the common factor of $2$ .

Factor $2$ out of $- 2$ .

$2 (- 1) \frac{25}{4}$

Factor $2$ out of $4$ .

$2 \cdot - 1 \frac{25}{2 \cdot 2}$

Cancel the common factor.

$2 \cdot - 1 \frac{25}{2 \cdot 2}$

Rewrite the expression.

$- 1 (\frac{25}{2})$

Step 4

Rewrite $- 1 (\frac{25}{2})$ as $- (\frac{25}{2})$ .

$- \frac{25}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- \frac{25}{2}$

Decimal Form:

$- 12.5$

Mixed Number Form:

$- 12 \frac{1}{2}$