what is the answer

Anything to a negative power is the same as 1 over that number to a positive power: 

$${{\mathtt{a}}}^{-{\mathtt{1}}} = {\frac{{\mathtt{1}}}{{{\mathtt{a}}}^{{\mathtt{1}}}}}$$

So for (1/4)^-1 . . . 

$$\frac{1}{(\frac{1}{4})^1} = \frac{1}{1}\times(\frac{4}{1})^1 = 4$$

Note that when you divide by a fraction you instead flip the denominator and numerator. When you get more practiced at this you can go straight from (1/4)^-1 to 4, as long as you know the process behind it.

In the same way . . .

$$\frac{1}{(\frac{1}{4})^2} = \frac{1}{1}\times(\frac{4}{1})^2 = \frac{4^2}{1^2} = 4^2 = 16$$

$$(\frac{1}{4})^2 = \frac{1^2}{4^2} = \frac{1}{16}$$