The total number of prime factors of (3 × 5)12 (2 × 7)10 (10)25 is ______.

Concept: Every composite number can be broken down into a product of primes raised to whole-number powers (its prime factorisation). The total number of prime factors of an expression — counting repetitions — is the sum of all these exponents once every composite base in the expression has been split into primes.

Application: Expand each bracket into its prime bases before combining exponents:

1. (3 × 5)12 = 312 × 512.

2. (2 × 7)10 = 210 × 710.

3. 1025 = (2 × 5)25 = 225 × 525.

4. Combine matching prime bases across all three expansions: 2's exponents add to 10 + 25 = 35, and 5's exponents add to 12 + 25 = 37, giving 235 × 312 × 537 × 710.

5. Sum every exponent to get the total count of prime factors: 35 + 12 + 37 + 10 = 94.

Cross-check: Re-adding the four exponents in a different grouping — (35 + 37) + (12 + 10) = 72 + 22 = 94 — confirms the same total, so no term was missed.

Result: 94 is not listed among the three specific values offered, so the expression's total prime-factor count corresponds to the “None of the above” option.