Answer:
The correct answer option is c. [tex]\frac{1}{9a^2}[/tex].
Step-by-step explanation:
We are given an expression [tex](27a^{-3})^{-\frac{2}{3} }[/tex] and we are supposed to simplify it.
We can also write [tex](27a^{-3})^{-\frac{2}{3} }[/tex] as [tex](\frac{3^3}{a^3} )^{-\frac{2}{3} }[/tex].
We know the power rule (a^m)^n=a^{mn} which means that to raise a power to a power you need to multiply the exponents.
So multiplying the exponents to get:
[tex]\frac{3^{(3.-\frac{2}{3})} }{a^{(3.\frac{2}{3})} }\\\\\frac{3^{-2}}{a^2}\\ \\\frac{1}{3^2a^2} \\\\\frac{1}{9a^2}[/tex]
Therefore, the correct answer option is c. [tex]\frac{1}{9a^2}[/tex].
