Try to answer the following:

**What is the units digit (last digit) of 2 ^{2011} ?**

**THE MAGIC REMAINDER TECHNIQUE**** **

(For numbers with a very large exponents)

To get the last digit of a number with a very large exponent:

**Step 1. **Get last 2 digits of the exponent.

**Step 2.** Divide by 4 and get remainder.

**Step 3. **The remainder becomes the new exponent.

Example:

- What is the units digit (last digit) of 2
^{2011}?

**Step 1.** 2^{2011 } –> 2^{11}

**Step 2.** Divide 11 by 4. Remainder = 3

**Step 3.** 2^{11} –> 2^{3} = 8

**Answer: ** Last digit = 8

**Exception to the Rule: **If the remainder is zero, exponent should be 4, not 0.

Example: 3^{12} –> 3^{4} = 8**1**. Last digit = 1.

**NOW, IT’S YOUR TURN!**

**What is the units digit of 3**^{2014}?**What is the units digit of 7**^{326}?**What is the units digit of 9**^{878}?**What is the units digit of 6**^{2015 }?**CHALLENGE:****What is the units digit of 123**^{2014}?

**Reflection for the Pro (if you are BRAVE enough!)**

^{ }If the base has more than one digit, what shortcut can you suggest?^{ }Think of a faster way if the base is 4 or 9. What if the base is 1, 5, 6 or 0?

**–Wacks Formula** 🙂

ShortCut #2: The Wacks Middle Finger Technique

*Disclaimer: The name of the formula is purely for fun, and does not discredit others who might have discovered the same formula independently.*

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