<p><a href="https://www.prepswift.com/quizzes/quiz/prepswift-exponents-and-unit-digits" target="_blank">Exponents and Unit Digits Exercise</a></p>
<p><strong>Important Note:</strong> At 00:45, Greg says "we would not call 5 the unit digit". This is incorrect, 5 is the unit digit here, what he meant to say was "we would not call 5.23 the unit digit". The unit digit would be 5 by itself.</p><p>Sometimes you're asked to find the unit digit of $n^x$, where $x$ is so large that if you tried to put it into your calculator, it would explode. Thus, you should memorize or be able to figure out the <strong><span style="color:#27ae60;">Exponent Unit Digit Patterns</span></strong>.</p>
<ul>
<li><span style="color:#e74c3c;">$0^n$</span>: always $0$</li>
<li><span style="color:#e74c3c;">$1^n$</span>: always $1$</li>
<li><span style="color:#e74c3c;">$2^n$</span>: $2, 4, 8, 6$, $2,4,8,6$ and so on
<ul>
<li><span style="color:#8e44ad;">repeats in blocks of $4$</span></li>
</ul>
</li>
<li><span style="color:#e74c3c;">$3^n$</span>: $3, 9, 7, 1$, $3,9,7,1$ and so on
<ul>
<li><span style="color:#8e44ad;">repeats in blocks of $4$</span></li>
</ul>
</li>
<li><span style="color:#e74c3c;">$4^n$</span>: $4, 6$, $4, 6$, $4, 6$ and so on
<ul>
<li><span style="color:#8e44ad;">repeats in blocks of $2$</span></li>
</ul>
</li>
<li><span style="color:#e74c3c;">$5^n$</span>: always $5$</li>
<li><span style="color:#e74c3c;">$6^n$</span>: always $6$</li>
<li><span style="color:#e74c3c;">$7^n$</span>: $7, 9, 3, 1$, $7, 9, 3, 1$ and so on
<ul>
<li><span style="color:#8e44ad;">repeats in blocks of $4$</span></li>
</ul>
</li>
<li><span style="color:#e74c3c;">$8^n$</span>: $8, 4, 2, 6$, $8, 4, 2, 6$ and so on
<ul>
<li><span style="color:#8e44ad;">repeats in blocks of $4$</span></li>
</ul>
</li>
<li><span style="color:#e74c3c;">$9^n$</span>: $9, 1$, $9, 1$, $9, 1$ and so on
<ul>
<li><span style="color:#8e44ad;">repeats in blocks of $2$</span></li>
</ul>
</li>
</ul>