Given the table values, Determine the base for the expoent function

To determine the value of the exponential function:
[tex]y=a^x[/tex]we use the first values from the table and plug them in the expression for the function:
[tex]\begin{gathered} \frac{1}{81}=a^{-\frac{1}{2}} \\ \frac{1}{a^2}=\frac{1}{81} \\ a^2=81 \\ a=\sqrt[]{81} \\ a=9 \end{gathered}[/tex]Therefore the base of the exponent function is 9