Answer
$$
8^{ x^{2} }=2^{x+4}
$$
The solution of the given equation is
$$
x=\frac{4}{3} \quad \text { or } \quad x=-1.
$$
Work Step by Step
$$
8^{ x^{2} }=2^{x+4}
$$
Since the bases must be the same, write 8 as $2^{3 }$ giving
$$
\begin{aligned} 8^{ x^{2} }&=2^{x+4} \\\left(2^{3}\right)^{x^{2}} &=2^{x+4} \\ 2^{3 x^{2}} &=2^{x+4} \\ 3 x^{2} &=x+4 \\ 3 x^{2} &-x-4=0 \\(3 x-4)(x+1) &=0 \\ x=\frac{4}{3} & \text { or } \quad x=-1 \end{aligned}
$$
So, the solution of the given equation is
$$
x=\frac{4}{3} \quad \text { or } \quad x=-1.
$$
