If m and n `(n gt 1)` are whole numbers such that `m^(n)=121`, the value of `(m-1)^(n+1)` is

Options

A. 1
B. 10
C. 121
D. 1000

Answer

To solve the problem step by step, we will follow these instructions:

1. **Identify the given equation**: We know that \( m^n = 121 \) and \( n > 1 \).

2. **Express 121 in terms of powers**: We can rewrite 121 as \( 11^2 \). Thus, we have:
\[ m^n = 11^2 \]

3. **Determine possible values for m and n**: Since \( m^n = 11^2 \), we can deduce possible values for \( m \) and \( n \). The simplest way is to set \( m = 11 \) and \( n = 2 \) because:
\[ 11^2 = 121 \]

4. **Verify the conditions**: We need to ensure that both \( m \) and \( n \) are whole numbers and that \( n > 1 \). Here, \( m = 11 \) (a whole number) and \( n = 2 \) (also a whole number and greater than 1), so the conditions are satisfied.

5. **Calculate \( (m-1)^{(n+1)} \)**: Now that we have \( m = 11 \) and \( n = 2 \), we can calculate:
\[ (m - 1)^{(n + 1)} = (11 - 1)^{(2 + 1)} = 10^3 \]

6. **Compute the final value**: Finally, we compute \( 10^3 \):
\[ 10^3 = 1000 \]

Thus, the value of \( (m-1)^{(n+1)} \) is **1000**.