Answer:
The correct answer option is [tex]\frac{25}{9}[/tex].
Step-by-step explanation:
We are given the following expression and we are to evaluate it when [tex]a = 5[/tex] and [tex]k = -2[/tex]:
[tex][\frac{3^2a^{-2}}{3a^{-1}} ]^k[/tex]
Substituting the given values of [tex] a [/tex] and [tex] k [/tex] to get:
[tex][\frac{3^2(5)^{-2}}{3(5)^{-1}} ]^{-2}[/tex]
[tex]\frac{3^{(2\times -2)}.5^{(1\times-2)}}{3^{(-1\times-2)}.5^{(2\times-2)}}[/tex]
[tex]\frac{3^{-4}.5^{-2}}{3^{-2}.5^{-4}}[/tex]
[tex]3^{-2}.5^2[/tex]
[tex] \frac { 1 } { 3 ^ 2 } . 2 [/tex]
[tex] \frac { 1 } { 9 } . 2 5 [/tex]
[tex] \frac { 2 5 } { 9 } [/tex]
