The dynamic power consumed by a CMOS circuit takes the following form.

α is how often signals switch, C is the capacitance being charged and discharged, V is the supply voltage, and f is the clock frequency. The decisive thing about this equation is that voltage, and only voltage, enters squared.

Halve the voltage and the power falls to a quarter. Halve the frequency and the power only falls by half. That is why low-power design reaches for the voltage first.