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In this paper, a study on the end-to-end performance of multihop free-space optical wireless systems over turbulence-induced fading channels, modeled by the gamma-gamma distribution, is presented. Our analysis is carried out for systems employing amplify-and-forward channel-state-information-assisted or fixed-gain relays. To assess the statistical properties of the end-to-end signal-to-noise ratio for both considered systems, we derive novel closed-form expressions for the moment-generating function, the probability density function, and the cumulative distribution function of the product of rational powers of statistically independent squared gamma-gamma random variables. These statistical results are then applied to studying the outage probability and the average bit error probability of binary modulation schemes. Also, for the case of channel-state-information-assisted relays, an accurate asymptotic performance analysis at high SNR values is presented. Numerical examples compare analytical and simulation results, verifying the correctness of the proposed mathematical analysis.