Number Theory
# Modular Arithmetic Operations

As we've now covered modular addition and modular multiplication (repeated modular addition), the next operation to consider is repeated modular multiplication, aka **modular exponentiation!**

Given that \( 9 \equiv 2 \pmod{7} \), what is \[ 9 \times 9 \times 9 \times 9 \times 9 \pmod{7}? \]

What is \( 2 ^ {15} \pmod{11} ?\)

What is \( 5 ^ {34} \pmod{31} ?\)

Which of the following is congruent to \[ \large 7^{7^{7^{7^7}}} \pmod {10}? \]

What is \( 2 ^ {7} \pmod{10} ?\)

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