If p varies inversely as the cube of q and q varies directly as the square of r, what is the relationship between p and r?

If p varies inversely as the cube of q and q varies directly as the square of r, what is the relationship between p and r?

Answer Details

P ∝ 1/q3
P = K/q3
q3 = K/P
q = K/p1/3
But q ∝ r2
q = Kr2K/p1/3 = Kr2
r2 = K/p1/3 x 1/K
r2 = 1/p1/3
r = (1/p1/3)2
r = 1/p1/6
r ∝ 1/p1/6
∴ r varies inversely as 6√P