For this case we must simplify the following expression:
[tex](3 ^ {-2}) ^ 4[/tex]
By definition of power properties we have to:[tex]a ^ {- 1} = \frac {1} {a ^ 1} = \frac {1} {a}[/tex]
So, rewriting the expression we have:
[tex](\frac {1} {3 ^ 2}) ^ 4 = \frac {1 ^ 4} {(3 ^ 2) ^ 4} = \frac {1} {(3 ^ 2) ^ 4}[/tex]
By definition of power properties we have:
[tex](a ^ n) ^ m = a ^ {n * m}[/tex]
So:
[tex]\frac {1} {(3 ^ 2) ^ 4} = \frac {1} {3 ^ 8}[/tex]
Answer:
Option D
