Answer
a. A. $\frac{25}{4}$
b. A. $\frac{25}{4}$
c. B. $-\frac{25}{4}$
d. B. $-\frac{25}{4}$
Work Step by Step
According to the definition of negative exponents $a^{-n}=\frac{1}{a^{n}}$ (where $a\ne0$).
Therefore,
a. $(\frac{2}{5})^{-2}=\frac{1}{(\frac{2}{5})^{2}}=\frac{5^{2}}{2^{2}}=\frac{25}{4}$
b. $(-\frac{2}{5})^{-2}=\frac{1}{(-\frac{2}{5})^{2}}=\frac{1}{(-1\times\frac{2}{5})^{2}}=(-1)^{2}\times\frac{5^{2}}{2^{2}}=1\times\frac{25}{4}=\frac{25}{4}$
c. $-(\frac{2}{5})^{-2}=-\frac{1}{(\frac{2}{5})^{2}}=-\frac{5^{2}}{2^{2}}=-\frac{25}{4}$
d. $-(-\frac{2}{5})^{-2}=-\frac{1}{(-\frac{2}{5})^{2}}=-\frac{1}{(-1\times\frac{2}{5})^{2}}=-((-1)^{2}\times\frac{5^{2}}{2^{2}})=-(1\times\frac{25}{4})=-(\frac{25}{4})=-\frac{25}{4}$
