Find the value of the following
If a=3 and b=4, find `b^(a)-a^(b)`

Answer

To solve the problem, we need to find the value of \( b^a - a^b \) given that \( a = 3 \) and \( b = 4 \).

### Step-by-Step Solution:

1. **Identify the values of a and b**:
- We have \( a = 3 \) and \( b = 4 \).

2. **Calculate \( b^a \)**:
- We need to calculate \( b^a \), which is \( 4^3 \).
- This means multiplying 4 by itself 3 times:
\[ 4^3 = 4 \times 4 \times 4 \]
- First, calculate \( 4 \times 4 = 16 \).
- Then, multiply 16 by 4:
\[ 16 \times 4 = 64 \]
- Therefore, \( b^a = 64 \).

3. **Calculate \( a^b \)**:
- Now, we need to calculate \( a^b \), which is \( 3^4 \).
- This means multiplying 3 by itself 4 times:
\[ 3^4 = 3 \times 3 \times 3 \times 3 \]
- First, calculate \( 3 \times 3 = 9 \).
- Next, multiply 9 by 3:
\[ 9 \times 3 = 27 \]
- Finally, multiply 27 by 3:
\[ 27 \times 3 = 81 \]
- Therefore, \( a^b = 81 \).

4. **Subtract \( a^b \) from \( b^a \)**:
- Now we need to find \( b^a - a^b \):
\[ 64 - 81 \]
- Performing the subtraction gives:
\[ 64 - 81 = -17 \]

5. **Final Answer**:
- Thus, the value of \( b^a - a^b \) is \( -17 \).

### Summary:
The final answer is:
\[ b^a - a^b = -17 \]