Find the value of xa + yb, if ay = 19683, where y is a multiple of a and bx = 1024, where b is a factor of x. a, b, x and y being positive integers:
ay = 19683
⇒ 3⁹ = 27³ = (19683)¹ = 19683
As y is a multiple of a, a = 3, y = 9, bx = 1024
⇒ 2¹⁰ = 4⁵ = 32² = (1024)¹ = 1024
As b is a factor of x, b = 2, x = 10
Now, xa + yb
⇒ 10³ + 9² = 1000 + 81 = 1081.