Answer
K is the equilibrium constant in terms of concentration, while Kp is the equilibrium constant in terms of partial pressures.
K = Kp when the sum of the coefficients of products is equal to the same of reactants.
K $\ne$ Kp when the sum of the coefficients of products is different than the same of reactants.
The new K is equal to the initial K to the power of 3. $K' = K^3$
The new Kp is equal to the inverse of the initial Kp: $Kp' = 1/Kp$
Work Step by Step
See sections 12-2 and 12-3.