Units Digits & Cycles

The last digits of repeated powers often form periodic residue cycles, so a huge exponent can be replaced by its position in a short cycle.

What you'll learn

  • Generate and verify a units-digit cycle by repeated multiplication modulo 10.
  • Reduce a large exponent to a correctly indexed cycle position.
  • Handle remainder zero as the final slot of a one-indexed power cycle.
  • Track and combine separate cycles in sums of powers.

Before you start

Loading guided lesson

Keep exploring