This paper presents analytical closed-form expressions that uncover the contributions of nodal active-and reactive-power injections to the active-and reactive-power flows on transmission lines in an AC electrical network. Paying due homage to current-and voltage-divider laws that are similar in spirit, we baptize these as the power divider laws. Derived from a circuit-theoretic examination of AC power-flow expressions, the constitution of the power divider laws reflects the topology and voltage profile of the network. We demonstrate the utility of the power divider laws to the analysis of power networks by highlighting applications to transmission-network allocation, transmission-loss allocation, and identifying feasible injections while respecting line active-power flow set points.