Final answer:
The value of x that makes the equation 8¹² * 8⁻²⁰ = 8ˣ true is x = -8.
Step-by-step explanation:
To solve the equation 8¹² * 8⁻²⁰ = 8ˣ, we can use the property of exponents which states that when we multiply numbers with the same base, we add the exponents. So, 8¹² * 8⁻²⁰ can be rewritten as 8^(12+(-20)) = 8ˣ. Simplifying the exponents, we get 8⁻⁸ = 8ˣ. Since the bases are the same, the exponents must be equal, so x = -8.