given expression,
[tex](w^0\ast x^{-3})^{-2}[/tex]let us simplify,
[tex]\begin{gathered} (w^0\ast x^{-3})^{-2} \\ =\frac{1}{(w^0\ast x^{-3})^2} \\ =\frac{1}{w^0}\ast\frac{1}{(x^{-3})^2} \\ =1\ast\frac{1}{x^{-6}} \\ =\frac{1}{\frac{1}{x^6}} \\ =x^6 \end{gathered}[/tex]the base is x.
the exponent is 6.