If m,n are the positive integers `(n gt 1)` such that `m^n = 121` , then value of `(m-1)^(n +1)` is :

Options

A. 12321
B. 1
C. 729
D. 11

Answer

To solve the problem step by step, we start with the given equation:

1. **Given Equation**:
\[ m^n = 121 \]
where \( m \) and \( n \) are positive integers and \( n > 1 \).

2. **Identify the Value of 121**:
We know that \( 121 \) can be expressed as:
\[ 121 = 11^2 \]

3. **Set Up the Equation**:
Since \( m^n = 121 \), we can rewrite it as:
\[ m^n = 11^2 \]

4. **Finding Possible Values of \( m \) and \( n \)**:
Given that \( n > 1 \), we can set \( n = 2 \) and \( m = 11 \) because:
\[ 11^2 = 121 \]
This satisfies the condition that both \( m \) and \( n \) are positive integers.

5. **Calculate \( m - 1 \)**:
Now we need to find \( m - 1 \):
\[ m - 1 = 11 - 1 = 10 \]

6. **Calculate \( n + 1 \)**:
Next, we calculate \( n + 1 \):
\[ n + 1 = 2 + 1 = 3 \]

7. **Final Calculation**:
Now we need to compute \( (m - 1)^{(n + 1)} \):
\[ (m - 1)^{(n + 1)} = 10^3 \]
Calculating \( 10^3 \):
\[ 10^3 = 1000 \]

Thus, the final answer is:
\[ \boxed{1000} \]