# 1. Suppose A = B^nC^m, where A has dimensions LT, B has dimensions L2T−1, and C has dimensions LT2. Then the exponent’s n and m have the values?

`A = B^n C^m`

Where `A = LT` ; `B = L^2T^-1` and `C= LT^2`

Arrange the equation first by substituting the terms given.

`[L][T] = ([L]^2 [T]^-1)^n ([L] [T]^2)^m`

`[L][T] = [L]^(2n+m) [T]^(-n + 2m)`

eq 1 ->  `1 = 2n + m`          --> `1 = 2n + m`

eq 2 -> `(1 = -n+ 2m)*2` --> `2 = -2n + 4m`    add
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`3 = 5m`

`m = 3/5`

substitute `m = 3/5` to any of the two equations.

eq 1-> `1 = 2n + m`

`1 = 2n + (3/5)`

`1 -3/5 = 2n`

`2/5 = 2n`

`n = 1/5`

Therefore the values of n and m are 1/5 and 3/5 respectively.