Question

if 1125 =3^m × 5^n, find m & n

Answer 1

prime factorisation of 1125=5×5×5×3×3
so 1125 = 5^3×3^2
m = 2 n = 3

Answer 2

$= > 1125 = {3}^{m} \times {5}^{n} \\ \\ = > 3 \times 3 \times 5 \times 5 \times 5 = {3}^{m} \times {5}^{n} \\ \\ = > {3}^{2} \times {5}^{3} = {3}^{m} \times {5}^{n}$
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BY COMPARISON WE GET

=> m = 2

=> n = 3
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