The efficiency of a Carnot (eta (C)) cycle is independent of the physical properties of the working gas. Therefore, eta (C) does not change due to quantum degeneracy of the gas. On the other hand, cycle work depends on the physical properties of the working gas since it is determined by the equation of state of the gas. Therefore, cycle work can be influenced by the quantum degeneracy of working gas. Here, Carnot power cycles working with ideal Bose and Fermi gases are examined under quantum degeneracy conditions. They are called Bose and Fermi Carnot cycles respectively. Cycle works of Bose and Fermi Carnot cycles (W-B and W-F) are derived. By dividing these works into the work of the classical Carnot power cycle (W-C), which works with classical ideal gas, work ratios are defined as R-W(B) = W-B/W-C and R-W(F) = W-F/W-C. Variations of R-W(B) and R-W(F) with high temperature of the cycle (T-H) are examined for a given temperature ratio tau = T-L/T-H and specific volume ratio r(v) = v(H)/v(L). It is shown that R-W(B) > 1 for some values of T-H while R-W(F) <1 for all values of T-H. At high T-H values, R-W(B) and R-W(F) go to unity. For an optimum value of T-H, it is seen that R-W(B) has a maximum, which is greater than unity and cannot be predicted by the classical ideal gas approximation. At the quantum degeneracy conditions, consequently, it is possible to produce more network output per cycle when a Bose gas is used as the working gas in a Carnot power cycle. For refrigeration and heat pump Carnot cycles, the use of a Bose gas persists to provide an advantage since it causes the heat pumped per cycle to increase. However, the use of a Fermi gas is always disadvantageous since it causes the network output in a power cycle and the heat pumped in the refrigeration and heat pump cycles to decrease.