Writing a number as m^n: n must divide every prime exponent

CAT has tested this idea 3 times across 3 papers, from 2018 to 2024. Solve one, and the others are the same method with different numbers or wording, which is why repeated concepts are the most efficient thing to practise.

Question	What it asks	Answer
CAT 2024 Slot 2 · QA Q3	m^n = 2^25 × 3^40; n is 5	C
CAT 2023 Slot 2 · QA Q1	a^m b^n = 144^145; maximise n − m	C
CAT 2018 Slot 2 · QA Q7	N^N = 2^160; largest power of 2 dividing N^2 + 2^N	10

Part of Logarithms & Exponents (55 questions since 2017).