Seniors, 70-plus, can strengthen their main core (the muscles deep within the abdominals and back that attach to the spine or pelvis or minor core muscles that include your lats, traps and glutes) with plank exercises.
As you’re beginning this type of movement, it is recommended to try a modified plank, using an elevated surface and extending forward and back. Variations on this include tightening your torso and doing small push-ups.