Answer
$x=-1,\dfrac{-1}{3}$
Work Step by Step
Re-write the given equation as: $(3^2)^{2x} \cdot (3^3)^{x^2}=3^{-1} ...(1)$
We know that $a^{m} \cdot a^n =a^{m+n}$
So, we can write equation (1) as: $3^{4x+3x^2}=3^{-1}$
Use the rule power rule: $a^p=a^q$ .
We can see that the base $a=3$ is the same on both sides of the equation.
So, the exponents will also be equal.
This implies that $p=q$
Therefore, $4x+3x^2=-1 \\ 3x^2+4x+1=0 \\ (3x+1)(x+1)=0$
By the zero-product property, we have: $x=-1,\dfrac{-1}{3}$
