Evaluate Using the Given Value f(-2)=-(5/4)^-2

$f (- 2) = - {(\frac{5}{4})}^{- 2}$

Step 1

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

$f (- 2) = - {(\frac{4}{5})}^{2}$

Step 2

Apply the product rule to $\frac{4}{5}$ .

$f (- 2) = - \frac{4^{2}}{5^{2}}$

Step 3

Raise $4$ to the power of $2$ .

$f (- 2) = - \frac{16}{5^{2}}$

Step 4

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

$f (- 2) = - \frac{16}{25}$