Super Pow - Insight

The key insight: $a^{1234} = a^{1230} \times a^4 = (a^{123})^{10} \times a^4$. You can process the exponent digit by digit from left to right.

For each digit $d$, raise the current result to the 10th power, then multiply by $a^d$. Apply mod at every step to keep numbers small.

This uses the property $(x \times y) \mod m = ((x \mod m) \times (y \mod m)) \mod m$ that you learned earlier.