How can I prove i = j = k = 1 in Peter's energy equation?

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To prove that i = j = k = 1 in Peter's energy equation E = (C)(M^i)(a^j)(d^k), one must utilize dimensional analysis. The dimensions of energy can be expressed in terms of mass (M), length (L), and time (T) as [E] = [M][L^2][T^-2]. By analyzing the dimensions of each component in the equation, it becomes evident that for the equation to be dimensionally consistent, the exponents i, j, and k must all equal 1. This conclusion is reached by equating the dimensions of the equation to those of energy.

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Panphobia
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I have been stuck on this problem for a while, I was looking at questions in a textbook, and could not figure this question out

"Peter came out with a new energy equation
E = (C)(M^i)(a^j)(d^k)
M is mass, a is acceleration, d is distance, and C is a dimensionless constant,
prove that i = j = k = 1"

How would you even start with this?

Regards, Panphobia
 
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Hint: dimensional analysis
 
I know that dimensional analysis is being able to state Mass, Length, and Time in terms of each other. But I do not know how that helps me prove that i = j = k = 1.
 
Write the dimension of energy, by means of the dimensions of mass, length and time!
 
Thank you everyone that helped me and gave me hints, I figured it out!
 

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