What would be the digit at the unit's place of \((13)^{547}\)?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 7
The unit digit of a power depends only on the unit digit of the base, here 3. The unit digits of the powers of 3 repeat in a cycle of four: 3, 9, 7, 1.
\(547=4\times136+3\), so the remainder on dividing the power by 4 is 3
The 3rd digit of the cycle is 7, so \((13)^{547}\) ends in 7