For integer values of a and b, b^a = 8. The ratio of a to b is equivalent to the ratio of c to d, where c and d are integers. What is the value of c when d = 10?

The only integer values to fit b^a = 8 would be 2^3, knowing this you can set up a proportion where

3:2 = c:10

c is then equal to 10/2 * 3

15

Bᵃ = 8, but 8 = 2³

then

bᵃ = 2³ and a = 3 and b = 8

a/b = c/d

3/8 = c/10. Cross multiplication: → 8c = 3x10 → 8c = 30

and c = 30/8 = 15/4

Proof:

3/8 = (15/4) / 10

3/8 = 15/40 and 15/40 = (3x5) / (8x5) = 3/8