If 1125 = 3^m × 5^n ;find the value of m and n.​

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  m = 2

  n = 3

Step-by-step explanation:

1125 = 9·125 = 3^2 · 5^3

  m = 2

  n = 3

Additional comment

Using divisibility rules, you can keep dividing by the obvious factors until the quotient is 1.

  1125/5 = 225

  225/5 = 45

  45/5 = 9

  9/3 = 3

  3/3 = 1 . . . . . . 5 is a factor 3 times; 3 is a factor 2 times.

The sin(A) goes with 'a'

sin(B) goes with b

sin(C) goes with c

Each angle goes with the corresponding side to form the three fractions shown. You can break up that triple equation into smaller equations such as and and

Note: if you apply the reciprocal to all three sides, then you'll get an equivalent equation. I'm using the rule that A/B = C/D is the same as B/A = D/C.