Evaluate $\frac{\frac{1}{1}}{\frac{1}{5^{-2}}}$

Question

I solved a question in the Manhattan GRE 5 pound book (specifically the 11th question in the Exponents and Roots section). I evaluated $\frac{\frac{1}{1}}{\frac{1}{5^{-2}}}$ as $5^{-2}$ and then $\frac{1}{25}$. But the solution given in the book evaluates it as $5^2$ which is $25$. Can anyone explain this?

Answer 1

It is possible that the book intended to write the expression $$\displaystyle\frac{1}{\frac{1}{\frac{1}{5^{-2}}}}$$ This evaluates to $$\displaystyle\frac{1}{\frac{1}{\frac{1}{5^{-2}}}}=\frac{1}{\frac{1}{5^2}}=5^2=25$$

Answer 2

The explanation is that the book is in error (assuming the question is accurately stated).

$$\Large{\frac{\frac{1}{1}}{\frac{1}{5^{-2}}}}=\Large{\frac{1}{\frac{1}{5^{-2}}}}=\frac{1}{5^{2}}=\frac{1}{25}$$