To solve this problem, we will use the following properties of exponents:
[tex]\begin{gathered} (a^n)^m=a^{n\times m}, \\ a^na^m=a^{n+m}, \\ (ab)^n=a^nb^n. \end{gathered}[/tex]
Using the first and last properties, we get:
[tex]\frac{(3x^{-2})^{-2}}{(-3x^{-3})(-\frac{1}{3}x^2)^3}=\frac{3^{-2}x^{-2\times-2}}{-3x^{-3}(-\frac{1}{3})^3x^{2\times3}}.[/tex]
Simplifying the above result, we get:
[tex]\frac{3^{-2}x^4}{-3x^{-3}(-\frac{1}{3^3})x^6}.[/tex]
Using the second property and simplifying we get:
[tex]\frac{x^4}{-3^3(-\frac{1}{3^3})x^{-3}x^6}=\frac{x^4}{x^{-3+6}}=\frac{x^4}{x^3}=x.[/tex]
Answer:
[tex]x.[/tex]
