Three letters can be posted in five letter boxes in `3^(8)` ways.

Answer

To solve the problem of how many ways three letters can be posted in five letter boxes, we can follow these steps:

### Step 1: Understand the Problem
We have three letters and five letter boxes. Each letter can be placed in any of the five boxes.

### Step 2: Determine the Choices for Each Letter
For each letter, we have 5 choices (since there are 5 letter boxes).

### Step 3: Calculate the Total Combinations
Since the placement of each letter is independent of the others, we can multiply the number of choices for each letter:
- For Letter 1, there are 5 choices.
- For Letter 2, there are also 5 choices.
- For Letter 3, there are again 5 choices.

Thus, the total number of ways to post the three letters is:
\[ 5 \times 5 \times 5 = 5^3 \]

### Step 4: Simplify the Expression
Calculating \(5^3\):
\[ 5^3 = 125 \]

### Step 5: Conclusion
The total number of ways to post the three letters in the five letter boxes is 125.

### Step 6: Verify the Given Statement
The problem states that the letters can be posted in \(3^8\) ways. We calculated it to be \(5^3\), which is 125. Since \(3^8\) is much larger than 125, we conclude that the given statement is false.

### Final Answer
The total number of ways to post three letters in five letter boxes is \(125\), and the statement claiming it to be \(3^8\) ways is incorrect.

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