If `m^(n)=169` what is the value of `(m+1)^((n-1))` ?

Options

A. 14
B. 13
C. 196
D. 170

Answer

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

1. **Given Equation**:
\[ m^n = 169 \]

2. **Factor 169**:
We can express 169 as a power of a prime number:
\[ 169 = 13^2 \]
This means we can set:
\[ m = 13 \quad \text{and} \quad n = 2 \]

3. **Substituting Values**:
Now we need to find the value of \((m + 1)^{(n - 1)}\):
\[ m + 1 = 13 + 1 = 14 \]
\[ n - 1 = 2 - 1 = 1 \]

4. **Calculating the Expression**:
Now we can substitute these values into our expression:
\[ (m + 1)^{(n - 1)} = 14^1 = 14 \]

5. **Final Answer**:
Thus, the value of \((m + 1)^{(n - 1)}\) is:
\[ \boxed{14} \]