If 3^(x^2)/3^4x=1/81 then x=?

Since the bases of the exponetials from the left side are
matching, we'll apply quotient property and we'll subtract the superscripts, such
as:

3^(x^2)/3^4x = 3^(x^2 -
4x)

We'll create matching bases both sides, therefore we'll
write 81 = 3^4

3^(x^2 - 4x) =
1/3^4

We'll apply the negative power
rule:

3^(x^2 - 4x) =
3^(-4)

Since the bases of the exponetials are matching,
we'll equate the exponents:

x^2 - 4x =
-4

We'll add 4 both sides:

x^2
- 4x+ 4 = 0

We'll recognize the perfect square (x -
2)^2:

(x - 2)^2 = 0 => x1 = x2 =
2

The equation has two equal solutions: x1 =
x2 = 2.