Final answer:
The given equation, -4a⁴a³ = 8, has one solution.
Step-by-step explanation:
The given equation is a quadratic equation of the form -4a⁴a³ = 8. To determine the number of solutions, we can first simplify the equation by multiplying the coefficients: -4a⁴a³ = 8 becomes -4a⁷ = 8. Then, we can divide both sides of the equation by -4 to isolate the variable, which gives us a⁷ = -2. Since any non-zero number raised to an odd power will have exactly one real solution, and in this case, a⁷ = -2 satisfies this condition, the answer is 2) one.