Evaluate 2(2/5)^-2

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

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

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

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 $2$ .

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

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{25}{2}$

The result can be shown in multiple forms.

Exact Form:

$\frac{25}{2}$

Decimal Form:

$12.5$

Mixed Number Form:

$12 \frac{1}{2}$