High School What exactly is Dimensional Analysis?

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Dimensional analysis is a mathematical technique used to check the consistency of equations by ensuring that both sides have the same dimensions. It involves expressing physical quantities in terms of their fundamental dimensions, such as mass (M), length (L), and time (T). The example provided illustrates how energy (E) can be expressed as a function of gravitational constant (G), mass (M), and radius (R) with specific exponents. This method is valuable for verifying solutions and deriving relationships between physical quantities. Overall, dimensional analysis serves as a powerful tool in physics for validating equations and enhancing understanding of physical relationships.
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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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