Determine the value of the exponents m and n for the equation to be dimensionally consistent. a) m = 3 n = −1

Okay, let's check the dimensional consistency of this equation: Length^m * Time^n For the equation to be dimensionally consistent, the left and right sides must have the same dimensions. Length has dimensions of L Time has dimensions of T Then: L^m * T^n must be dimensionless For L^m to be dimensionless, m must be 0. For T^n to be dimensionless, n must be -1. Therefore, the only value of m and n that makes the equation dimensionally consistent is: m = 0 n = -1 So the answer is: m = 0 n = -1 (a) is not a dimensionally consistent solution because m should be 0, not 3. Only when m=0, n=-1 is the equation dimensionally consistent with the left and right sides being dimensionless.