If 847 × 385 × 675 × 3025 = 3^a × 5^b × 7^c × 11^d then the value of ab - cd is

Solution (By Examveda Team)

847 × 385 × 675 × 3025 = 3^a × 5^b × 7^c × 11^d
LHS ⇒ 847 × 385 × 675 × 3025
= (7 × 11 × 11) × (5 × 7 × 11) × (3 × 3 × 3 × 5 × 5) × (5 × 5 × 11 × 11)
= 3³ × 5⁵ × 7² × 11⁵
= 3^a × 5^b × 7^c × 11^d
Compare value
a = 3; b = 5; c = 2; d = 5
⇒ ab - cd = 3 × 5 - 2 × 5 = 15 - 10 = 5