If momentum (P), area (A) and time (T) are taken to be fundamental quantities, then the dimensional formula for energy is:
[P²AT⁻²]
[PA⁻¹T⁻²]
[PA¹ᐟ²T⁻¹]
[P¹ᐟ²AT⁻¹]
Let [E] = [P]ˣ[A]ʸ[T]ᶻ
ML²T⁻² = [MLT⁻¹]ˣ [L²]ʸ [T]ᶻ
ML²T⁻² = MˣLˣ⁺²ʸT⁻ˣ⁺ᶻ
⇒ x = 1
⇒ x + 2y = 2
1 + 2y = 2
y = 1/2
−x + z = −2
−1 + z = −2
z = −1
[E] = [PA¹ᐟ²T⁻¹]
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