Given the expression:
[tex](a^{-2}b^3)^{-3}[/tex]We apply the product law below:
[tex](a^x)^y=a^{x\times y}[/tex]Therefore, we have:
[tex]\begin{gathered} =a^{-2\times-3}\times b^{3\times-3} \\ =a^6b^{-9} \end{gathered}[/tex]Next, apply the negative exponent law:
[tex]a^{-x}=\frac{1}{a^x}[/tex]Thus:
[tex]\begin{gathered} a^6b^{-9}=a^6\times\frac{1}{b^9} \\ =\frac{a^6}{b^9} \end{gathered}[/tex]