If `3^n = 27` then `3^(n - 2)` is:

Options

A. 3
B. `1/3`
C. `1/9`
D. `9`

Answer

To solve the equation \( 3^n = 27 \) and find the value of \( 3^{(n - 2)} \), we can follow these steps:

### Step 1: Rewrite 27 as a power of 3
We know that \( 27 \) can be expressed as a power of \( 3 \):
\[ 27 = 3^3 \]

### Step 2: Set the exponents equal
Since the bases are the same, we can set the exponents equal to each other:
\[ n = 3 \]

### Step 3: Substitute \( n \) into \( 3^{(n - 2)} \)
Now that we have found \( n \), we can substitute it into the expression \( 3^{(n - 2)} \):
\[ 3^{(n - 2)} = 3^{(3 - 2)} = 3^{1} \]

### Step 4: Calculate \( 3^{1} \)
Now we can calculate \( 3^{1} \):
\[ 3^{1} = 3 \]

### Final Answer
Thus, the value of \( 3^{(n - 2)} \) is:
\[ \boxed{3} \]

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