Question

For what value of n does (1/36)^n =216

Answer 1

1/36 is
`6^(-2)`, and 216 is
`6^(3)`

`6^(-2n) = 6^(3)`
-2n=3
n=-3/2

Answer 2

To find the value of
`n` that satisfies the equation, we follow the steps shown below:

`((1)/(36) )^n=216\\`

`((1)/(6^2) )^n=6^3\\=>(6^(-2))^n=6^3`

The last statement above is true because for indices,
`(1)/(x^n) =x^(-n)`, also
`(x^a)^b=x^(ab)` so,

`6^(-2n)=6^3\\=>-2n=3\\=>n=-(3)/(2).`

So
`n=-(3)/(2)` is the only value of
`n` that satisfied this equation. The second option is the correct answer.