The highest power of 17 which can divide exactly the following:
(18² - 1) (18⁴ - 1) (18⁶ - 1) (18⁸ - 1) . . . . (18¹⁶ - 1) (18¹⁸ - 1) is :

Explanation:-

Total number of terms in expression = 9.
(18² - 1) = (18 - 1) × (18 + 1).
(18⁴ - 1) = (18² + 1) × (18² - 1) = (18² + 1) × (18 - 1) × (18 + 1).
(18⁶ - 1) = [(18³)² -1] = (18³ + 1) (18³ - 1) = 17 × k and so on.
Hence, there will be 9 times 17 in the whole expression as each term of expression gives one 17. Therefore for maximum power of 17 will be 9.