If `m` and `n` are whole numbers such that, `m^n = 169`, then the value of `(m-3)^(n+1)` is

Options

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

Answer

To solve the problem step by step, we need to find the values of \( m \) and \( n \) such that \( m^n = 169 \), and then calculate \( (m-3)^{(n+1)} \).

### Step 1: Identify the values of \( m \) and \( n \)

We know that:
\[ m^n = 169 \]
We can express 169 as a power:
\[ 169 = 13^2 \]
This means we can set:
\[ m = 13 \quad \text{and} \quad n = 2 \]

### Step 2: Calculate \( m - 3 \)

Now that we have \( m \):
\[ m - 3 = 13 - 3 = 10 \]

### Step 3: Calculate \( n + 1 \)

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

### Step 4: Calculate \( (m - 3)^{(n + 1)} \)

Now we substitute the values into the expression \( (m - 3)^{(n + 1)} \):
\[ (m - 3)^{(n + 1)} = 10^3 \]

### Step 5: Calculate \( 10^3 \)

Finally, we calculate \( 10^3 \):
\[ 10^3 = 1000 \]

### Final Answer

Thus, the value of \( (m - 3)^{(n + 1)} \) is:
\[ \boxed{1000} \]