If 102/5 × 108/5 = 10n, the value of n is :

∵ 10^2/5 × 10^8/5 = 10ⁿ
⇒ 10^{2/5 + 8/5} = 10ⁿ
⇒ 10^10/5 = 10ⁿ ⇒ 10² = 10ⁿ ⇒ n = 2
Hence, the value of n is 2.