How do you simplify 1/4^-2 ?

Express the denominator as a fraction such as $\frac{1}{\left(\frac{1}{4} ^ \left(2\right)\right)}$
Knowing that ${4}^{2} = 16$, multiply the denominator and numerator by the reciprocal:
$\frac{1}{\left(\frac{1}{4} ^ \left(2\right)\right)} = \frac{\left(1\right) \cdot \left(\frac{16}{1}\right)}{\cancel{\left(\left(\frac{1}{16}\right) \cdot \left(\frac{16}{1}\right)\right)}} = 16$
The "trick" here is to express ${4}^{- 2}$ as a fraction of integers.