If `3^n` = 27 then `3^(n-1)` is :

Options

A. 9
B. 6
C. 0
D. 3

Answer

To solve the problem, we need to find the value of \( 3^{n-1} \) given that \( 3^n = 27 \).

### Step-by-step Solution:

1. **Identify the value of \( 27 \) in terms of base \( 3 \)**:
\[ 27 = 3^3 \]
This means we can rewrite the equation \( 3^n = 27 \) as:
\[ 3^n = 3^3 \]

2. **Since the bases are the same, we can equate the exponents**:
\[ n = 3 \]

3. **Now, we need to find \( 3^{n-1} \)**:
\[ n - 1 = 3 - 1 = 2 \]
So we have:
\[ 3^{n-1} = 3^2 \]

4. **Calculate \( 3^2 \)**:
\[ 3^2 = 9 \]

Thus, the value of \( 3^{n-1} \) is \( 9 \).

### Final Answer:
\[ 3^{n-1} = 9 \]