Find out the LCM of `3^(5), 3^(11), 3^(-11) and 3^(14)` ______
A. `3^(5)`
B. `3^(11)`
C. `3^(-11)`
D. `3^(14)`

Options

A. D
B. A
C. B
D. C

Answer

To find the LCM (Least Common Multiple) of the numbers \(3^5\), \(3^{11}\), \(3^{-11}\), and \(3^{14}\), we can follow these steps:

### Step 1: Identify the Exponents
The numbers we have are:
- \(3^5\)
- \(3^{11}\)
- \(3^{-11}\)
- \(3^{14}\)

### Step 2: Find the Highest Exponent
Since the base is the same (which is 3), the LCM will be determined by the highest exponent among these numbers.

The exponents are:
- \(5\)
- \(11\)
- \(-11\)
- \(14\)

### Step 3: Compare the Exponents
Now, we compare the exponents:
- The highest exponent among \(5\), \(11\), \(-11\), and \(14\) is \(14\).

### Step 4: Write the LCM
Thus, the LCM of \(3^5\), \(3^{11}\), \(3^{-11}\), and \(3^{14}\) is:
\[ LCM = 3^{14} \]

### Conclusion
The answer is \(3^{14}\).

### Final Answer
D. \(3^{14}\)

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