Correct Answer - Option 1 : 84
Given:
(21)22 × (15)8 × (6)12
Formula used:
(ab)n = an × bn
Calculation:
(21)22 × (15)8 × (6)12
⇒ (3 × 7)22 × (3 × 5)8 × (2 × 3)12
⇒ 322 × 722 × 38 × 58 × 212 × 312
⇒ 342 × 722 × 58 × 212
Total prime factors = 42 + 22 + 8 +12 = 84
∴ The number of prime factors in (21)22 × (15)8 × (6)12 is 84.
Note:- Here total prime factors are asked. If we have to find the distinct prime numbers then our answer will be 4 (i.e. 2, 3, 5, 7)