Finding Planck time in terms of [G], [h], and [c]

[zeion]

Homework Statement

Find a set of 3 exponents a, b, g such that the quantity [G]^a [h]^b [c]^g has dimensions of time. In other words:
[T] = [G]^a [h]^b [c]^g
(hint: you should get 3 algebraic equations in the 3 unknowns a, b, g which are not that hard to solve. Now determine the socalled
Planck time from tPlanck = G^a h^b c^g. [3 Points].

Homework Equations

G = 6.67266 x 10^-11 m^3 kg^-1 s^-2
h = 6.62606896x10^-34 kg m^2 s^-1
c = 299,792,458 m s^-1

The Attempt at a Solution

I solved a = 1/2, b = 1/2, g = -5/2, which cancel out the dimensions other than [T],
and then I tried to calculate the value for Placnk time:

(6.67266 x 10^-11)^(1/2) (6.62606896x10^-34)^(1/2) (299,792,458)^(-5/2)
= 1.3512189 x10^-43

Which is not what it should be.. where did I make a mistake..?

 

[vela]

You used h rather than \hbar.

 

[Nexelos]

How did you find out those exact values of the exponents?