Question

If 1125 = 3^m x 5^n: find m and n.

Answer 1

1125=3^m x 5^n
(do prime factorisation of 1125)
3^2 x 5^3=3^m x 5^ n
On comparing
3^2=3^m. 5^3=5^n
2= m. 3=n
Hope my answer will help you

Answer 2

Answer :- m= 2 and n = 3.

Explanation :-

Given :-

If 1125= 3^m*5^n. find m and n

Finding the LCM of 1125 :-

$\begin{array}{r | l} 5 & 1125 \\ \cline{2-2} 5 & 225 \\ \cline{2-2} 5 & 45 \\ \cline{2-2} 3 & 9 \\ \cline{2-2} 3 & 3 \\ \cline{2-2} & 1 \end{array}$

LCM is :-

${5}^{3} \times {3}^{2}$

$1125 = {3}^{m} \times {5}^{n}$

On comparison :-

${3}^{m} \times {5}^{n} = {5}^{3} \times {3}^{2}$

Hence, m= 2 and n = 3.