Let's clean the expression for [tex] \frac{a}{b} [/tex]: first of all, every number raised to the power of zero is one, so it can be ignored, since it is a multiplicative factor.
Moreover, we can use the rule for negative exponents
[tex] \left( \frac{a}{b} \right) ^ {-n} = \left( \frac{b}{a} \right) ^ {n} [/tex]
To write the expression for [tex] \frac{a}{b} [/tex] as
[tex] \frac{a}{b} = \left( \frac{3}{2}\right)^3x = \frac{27}{8} x [/tex]
So, [tex] \left( \frac{a}{b} \right) ^ {-3} = \left(\frac{27}{8} x\right)^{-3} = \left( \frac{8}{27} \right)^3 \frac{1}{x^3} = \frac{8^3}{27^3x^3} = \frac{512}{19683x^3}[/tex]
