Physics

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


SOLUTION

Comparing the exponents of  $$\mathrm { M } , L$$  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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