Solve for n:

Question

((3^n)^n*(3^n)^-1) / 81 = 1

Answer (n) = -1, 4

I have no idea how n = -1, 4. Also, please don't ask if the answers are actually wrong or not, they are directly from the text book.

Answer 1

((3^n)^n*(3^n)^-1) / 81 = 1
3^(2n) * 3^-n = 81
3^n = 81
3^n = 3^4
n = 4

testing the n = -1 solution

Left Side
= ( (3^-1)^(-1) * (3^-1)^-1 )/81
= (3^1 * 3^1 )/81
= 9/81
≠ 1

So according to the way you typed it, the book is wrong,

the only solution is n = 4

Answer 2

Alright, thanks so much for the help!