Finding values of constant by using Dimensional Analysis

[Byeongok]

Homework Statement

The speed v of sound in a gas depends on the density p and pressure P of the gass. If this dependence is in the form of a power law that is,

v = kp^aP^b

where k, a and b are constants (k a dimensionless one).
a. Determine by dimensional analysis the values of a and b.
b. There by rewrite the above equation in a simpler form.

Homework Equations

v = kp^aP^b

The Attempt at a Solution

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I started off by writing the dimensions in the equation

[L][T]^-1 = ( [M][L]^-3 )^a ( [M][L]^-1[T]^-2 )^b

From here, i think i have to try and find the values for a and b that allows the right hand side of the equation to match the left. Also in this situation, do i just leave K out of it?
Any help to proceed to next step towards the answer would be great.

 

[mfb]

From here, i think i have to try and find the values for a and b that allows the right hand side of the equation to match the left.

Right.

Also in this situation, do i just leave K out of it?

k is dimensionless, so it is irrelevant here.