If m and n are positive integers, then the digit in
the unit's place of $5^n$ + $6^m$ is always

Question

If m and n are positive integers, then the digit in
the unit's place of $5^n$ + $6^m$  is always

Accepted Answer

To determine the unit digit of $$ 5^n + 6^m $$, we analyze the unit digits of $$ 5^n $$ and $$ 6^m $$:

**Unit digit of $$ 5^n $$:**  
   The unit digit of any power of $$ 5 $$ is always $$ 5 $$. For example:  
   - $$ 5^1 = 5 $$, unit digit = $$ 5 $$  
   - $$ 5^2 = 25 $$, unit digit = $$ 5 $$  
   - $$ 5^3 = 125 $$, unit digit = $$ 5 $$, and so on.

**Unit digit of $$ 6^m $$:**  
   The unit digit of any power of $$ 6 $$ is always $$ 6 $$. For example:  
   - $$ 6^1 = 6 $$, unit digit = $$ 6 $$  
   - $$ 6^2 = 36 $$, unit digit = $$ 6 $$  
   - $$ 6^3 = 216 $$, unit digit = $$ 6 $$, and so on.

**Unit digit of $$ 5^n + 6^m $$:**  
   Adding the unit digits of $$ 5^n $$ and $$ 6^m $$:  
   - Unit digit of $$ (5 + 6) = 11 $$, so the unit digit is **1**.

Thus, for all positive integers $$ m $$ and $$ n $$, the unit digit of $$ 5^n + 6^m $$ is always **1**.

Answer

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