Dimensions of physical quantities

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Question

The dimensional formula of $\frac{{EJ}^{2}}{M^{5} G^{2}}$ where E, M, J and G denote energy, mass, angular momentum and gravitational constant is M^aL^bT^c. Then the value of c is

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Solution

$[\frac{{EJ}^{2}}{M^{5} G^{2}}] = \frac{({ML}^{2} T^{- 2}) {({ML}^{2} T^{- 1})}^{2}}{(M^{5}) {(M^{- 1} L^{3} T^{- 2})}^{2}} = M^{0} L^{0} T^{0}$

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