$M L T^{- 2} = k L^{a} {(L T^{- 1})}^{b} {(M L^{- 1} T^{- 1})}^{c}$
where $k$ is a dimensionless constant. Taking dimensions on both sides,
find value a, b and c

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Solution

Comparing the exponents of $M, L$ and $T$

$1 = c$

$1 = a + b - c$

$- 2 = - b - c$
Solving these equations $a = 1, b = 1$ and $c = 1$ .

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