Answer
$x=-4,2$
Work Step by Step
Re-write the given equation as: $(2^2)^{x} \cdot 2^{x^2}=2^{8} ...(1)$
We know that $a^{m} \cdot a^n =a^{m+n}$
So, we can write equation (1) as: $2^{2x+x^2}=2^{8}$
Use the rule power rule: $a^p=a^q$ .
We can see that the base $a=2$ is the same on both sides of the equation.
So, the exponents will also be equal.
This implies that $p=q$
Therefore, $2x+x^2=8 \\ x^2+2x-8=0 \\ (x+4)(x-2)=0$
By the zero-product property, we have: $x=-4,2$
