Live axle is the one through which power is transmitted to the wheels.
It can be either the front axle (in case of front wheel drive) or rear axle (in case of rear wheel drive).

Dead axle is the axle which only supports the wheels.
It does not transfer power or torque to the wheels whatsoever. In case of a front wheel drive, the rear axle is the dead axle, and in case of rear wheel drive, the front axle is dear axle.

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