`3^(18)+3^(15)` is divisible by

Options

A. `31`
B. `13`
C. `28`
D. `33`

Answer

To solve the problem \(3^{18} + 3^{15}\) and determine what it is divisible by, we can follow these steps:

### Step 1: Factor out the common term
We notice that both terms \(3^{18}\) and \(3^{15}\) have a common factor of \(3^{15}\). We can factor this out:

\[ 3^{18} + 3^{15} = 3^{15}(3^{3} + 1) \]

### Step 2: Simplify the expression inside the parentheses
Next, we simplify the expression inside the parentheses:

\[ 3^{3} + 1 = 27 + 1 = 28 \]

### Step 3: Combine the results
Now we can rewrite our expression using the results from the previous steps:

\[ 3^{18} + 3^{15} = 3^{15} \times 28 \]

### Step 4: Determine the divisibility
From the expression \(3^{15} \times 28\), we can see that \(3^{18} + 3^{15}\) is divisible by \(28\) (since it is multiplied by \(28\)).

### Conclusion
Thus, \(3^{18} + 3^{15}\) is divisible by \(28\).

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