With CMOS gates such as the Quad two-input mux 74HCT157 its best to tie the inputs to all unused gates or logic blocks to ground or Vcc and leave unused outputs open. This stops the unused inputs from floating into the active range and possibly causing the gate/logic to oscillate and so draw excessive power.
If you have unused inputs on the gates/logic which you ARE using then you have to tie them either high or low depending on the logic involved in order for your circuit to work correctly. Unused outputs on same should, again, just be left open.
This rule holds for both CMOS logic families and real TTL families such as 74LSXX, 74XX, 74Sxx, etc but in the case of TTL the power draw with unused gates can be minimized by tying the inputs high directly to Vcc or through a 1K resistor. As many as 20 inputs can be tied to the same resistor.