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Thermodynamics of ideal Fermi gas trapped in an external generic power lawpotential $U=\sum_{i=1} ^d c_i |\frac{x_i}{a_i}|^{n_i}$ are investigatedsystematically from the grand thermodynamic potential in $d$ dimensional space.These properties are explored deeply in the degenerate limit ($\mu>> K_BT$),where the thermodynamic properties are greatly dominated by Pauli exclusionprinciple. Pressure and energy along with the isothermal compressibilty is nonzero at $T=0K$, denoting trapped Fermi system is quite live even at absolutezero temperature. The nonzero value of compressibilty denotes zero pointpressure is not just a constant but depends on volume.

Thermodynamics of ideal Fermi gas under generic power law potential in $d$-dimension