In the table each value is half of the value above it. Continue the pattern: what are $2^0$ and 2⁻¹?

Going down, divide by 2 each time: $2^1=2$, so $2^0=2÷2=1$ and $2^{-1}=1÷2=\frac{1}{2}$. A zero exponent gives 1, not 0, and a negative exponent gives a fraction, not a negative number.