What is the reciprocal of $(-1/2)^k$? What is the reciprocal of $(-1/2)^k$?

The answer is meant to be $2^{-k}$ as if you flip something upside down the power becomes negative. However, I am not sure what happens to the negative in front of the fraction.
The reciprocal of $x$ is simply $\frac1x$. So the reciprocal of $(-\tfrac12)^k$ is $\frac1{(-\tfrac12)^k}$. 

You may also recall from the exponentiation laws that $(\frac1x)^y=x^{-y}$, and that the repciprocal of $x^y$ is $\frac1{x^y}=x^{-y}$.
This allows us to rewrite $(-\tfrac 12)^k$ as $(-2)^{-k}$, and then the reciprocal of this is $(-2)^k$. If $k$ is even, this simplifies to $2^k$; if $k$ is odd, it becomes $-2^k$.
The answer would look like $(-1)^k.2^{-k}$. The negative would depend if k is even or odd.