What exactly is Dimensional Analysis?

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DeltaForce
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Just what is dimensional analysis?
Can someone explain it to me exactly how dimensional analysis works (perhaps gives some examples.)
What use does it have? Is it a convenient way to check your solutions?

My teacher showed this example

E ~ G, M, R
[E] = k[G^α * M^β *R^γ]
Maybe someone can explain this.
 
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Thank you Greg!
 
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