3^(x^2+4x)=(1/9)^2

We'll start by using the negative power rule to the right
side:

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

Since
the bases are matching, we'll apply one to one rule:

x^2 +
4x = -4

We'll add 4 both
sideS:

x^2 + 4x + 4 = 0

We'll
apply quadratic formula:

x1 = [-4+sqrt(16 -
16)]/2

x1 = (-4+0)/2

x1 =
-2

x2 =
-2

The solution of the equation is x =
-2.