Show that `(P^(-5//6)rho^(1//2)E^(1//3))` is of the dimension of time. Here P is the pressure, `rho` is the density and E is the energy of a bubble).

Explanation

Dimension of Pressure = `[ML^(-1)T^(-2)]`
Dimension of density = `[ML^(-3)]`
Dimension of Energy = `[ML^(2)T^(-2)]`
By substituting in the given equation,
`=[ML^(-1)T^(-2)]^(-5//6) [ML^(-3)]^(1//2) [ML^(2)T^(-2)]^(1//3)`
`= M^(-5//6+1//2+1//3) L^(5//6-3//2+2//3)T^(5//3-2//3)`
`= M^(0)L^(0)T^(1) = [T]`