Number System Question 6 - CAT 2024

Step-by-Step Explanation

Perform prime factorization on the right side of the equation:

mⁿ = 2²⁵ × 3⁴⁰

To express the right side in the form mⁿ, find a common exponent for both prime factors. This common exponent must be a common divisor of the original powers, 25 and 40.

HCF(25,40) = 5

Rewrite the expression using the exponent 5:

mⁿ = ( 2⁵ )⁵ × ( 3⁸ )⁵ = ( 2⁵ × 3⁸ )⁵

mⁿ = (32 × 6561)⁵ = (209952)⁵

Since the problem states n > 1, we match the terms directly:

m = 209952, n = 5

m - n = 209952 - 5 = 209947

Correct Option: D