Question

Which is the value of this expression when a=5 and k=-2

Answer 1

Option C is correct.

Explanation:

We are given the expression:

`((3^2a^(-2))/(3a^(-1)))^k`

The value of a =5 and k = -2

Putting the values and solving

`=((3^2*5^(-2))/(3*5^(-1)))^-2\\=((3^(2-1))/(5^(-1+2)))^-2\\=((3^(1))/(5^(1)))^-2\\\\=((3)/(5))^-2\\if \,\,a^(-1) \,\,then\,\, 1/a\\=((3)^(-2))/((5)^(-2))\\ Can\,\,be\,\,written\,\,as\\\\=((5)^(2))/((3)^(2)) \\=(25)/(9)`

Option C is correct.