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Relativistic electrons are an essential component in many astrophysicalsources, and their radiation may dominate the high-energy bands. InverseCompton (IC) emission is the radiation mechanism that plays the most importantrole in these bands. The basic properties of IC, such as the total anddifferential cross sections, have long been studied; the properties of the ICemission depend strongly not only on the emitting electron distribution butalso on the properties of the target photons. This complicates thephenomenological studies of sources, where target photons are supplied from abroad radiation component. We study the spectral properties of IC emissiongenerated by a power-law distribution of electrons on a power-law distributionof target photons. We approximate the resulting spectrum by a broken-power-lawdistribution and show that there can be up to three physically motivatedspectral breaks. If the target photon spectrum extends to sufficiently lowenergies, $\varepsilon_{\mathrm{min}}< m_e^2c^4/E_{\mathrm{max}}$ ($m_e$ and$c$ are electron mass and speed of light, respectively;$\varepsilon_{\mathrm{min}}$ and $E_{\mathrm{max}}$ are the minimum/maximumenergies of target photons and electrons, respectively), then the high energypart of the IC component has a spectral slope typical for the Thomson regimewith an abrupt cutoff close to $E_{\mathrm{max}}$. The spectra typical for theKlein-Nishina regime are formed above $m_e^2c^4/\varepsilon_{\mathrm{min}}$. Ifthe spectrum of target photons features a cooling break, i.e., a change of thephoton index by $0.5$ at $\varepsilon_{\mathrm{br}}$, then the transition tothe Klein-Nishina regime proceeds through an intermediate change of the photonindex by $0.5$ at $m_e^2c^4/\varepsilon_{\mathrm{br}}$.

On the properties of inverse Compton spectra generated by up-scattering a power-law distribution of target photons