Hola

supongo

y = v_o * t - (1/2) g * t^2

[y] = L

*****************

[v_o] = L T^-1

[t] = T

[v_o * t] = L

*****************

[g] = L T^-2

[t^2] = T^2

[gt^2] = L

*****************

Hay dos sumandos con misma dimensión L

y el resultado tiene dimensión L

Sí, es correcta dimensionalmente.

b)

A^3 = B^2 C

B^2 = A^3 C^-1

B = A^(3/2) C^(-1/2)

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[A] = L^(1/3) / M^2 = L^(1/3) M^(-2)

[C] = T L / M = T L M^-1

[A^(3/2)] = L^( (1/3)(3/2) ) M^(-2 (3/2))

[A^(3/2)] = L^(1/2) M^(-3)

[C^(-1/2)] = T^(-1/2) L^(-1/2) M^(1/2)

[B] = L^((1/2) + (-1/2)) M^(-3) + (1/2)) T^(-1/2)

[B] = L^0 M^((-6/2) + (1/2)) T^(-1/2)

[B] = M^(-5/2) T^(-1/2)

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Verificamos

[B2 C] = L^1 M^((-5) + (-1)) T^((-1) + 1)

[B2 C] = L^1 M^(-6)

[A^3] = L^1 M^(-6)

Saludos

no se