Based on the pattern in the table, what is the value of a?

Negative powers always refer to a division. Negative exponents refer to how many times an unity is being divided. That's why
[tex]\begin{gathered} 2^{-6}=\frac{1}{2^6} \\ =\frac{1}{2\times2\times2\times2\times2\times2} \\ =\frac{1}{64} \end{gathered}[/tex]