(a) 5m.252m = 1252m - 1

=> 5m.54m = (53)2m - 1

=> 55m = 56m - 3

=> 5m = 6m - 3

=> m = 3

(b) 5m.25m.125m.625m = 530

=> (5.25.125.625)m = 530

=> (5.52.53.54)m = 530

=> 510m = 530

=> 10m = 30

=> m = 3

(a) 5^m.25^2m = 125^{2m - 1}

=> 5^m.5^4m = (5³)^{2m - 1}

=> 5^5m = 5^{6m - 3}

=> 5m = 6m - 3

=> m = 3

(b) 5^m.25^m.125^m.625^m = 5³⁰

=> (5.25.125.625)^m = 5³⁰

=> (5.5².5³.5⁴)^m = 5³⁰

=> 5^10m = 5³⁰

=> 10m = 30

=> m = 3