Final answer:
The value of a that makes F(x) = ax9/8 an antiderivative of f(x) = 18x1/8 is 16, obtained by applying the power rule of integration.
Step-by-step explanation:
The question involves determining the value of a that makes F(x) = ax9/8 an antiderivative of f(x) = 18x1/8. To find the antiderivative F(x) of a function f(x), we apply the power rule of integration, which states that F(x) = ∫f(x)dx. To apply the power rule, we increase the exponent by 1 and divide by the new exponent. Therefore, the antiderivative of 18x1/8 would be F(x) = 18 ∫x1/8dx = 18 × (1/(1/8 + 1))x1/8 + 1 = 18 × (8/9)x9/8. Simplifying, we get F(x) = 16x9/8. Comparing this formula with the given F(x) = ax9/8, we can determine that the value of a is 16.