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The user and the target have their Attack and Special Attack stats set to be equal to the average of the user and the target's Attack and Special Attack stats, respectively, rounded down. Stat stage changes are unaffected. The effect on each lasts until they faint or switch out.
Power Split could be used to set up a mixed attacker without using a nature that lowers Defense, Special Defense, or Speed, or to lower the power of a target with very unbalanced attacking stats. The setup turn kills this move's viability almost entirely, though. It's also incredibly situational...
Guard Split has the same effect, except on the Defense and Special Defense stats.