If a= -1 and b= 2 find :
` a^(b) xx b^(a)`

Answer

To solve the problem where \( a = -1 \) and \( b = 2 \), we need to find the value of \( a^b \times b^a \).

### Step-by-Step Solution:

1. **Identify the values of a and b**:
- Given \( a = -1 \) and \( b = 2 \).

2. **Calculate \( a^b \)**:
- We need to compute \( a^b = (-1)^2 \).
- Since \( (-1)^2 = 1 \) (because multiplying -1 by itself gives 1).

3. **Calculate \( b^a \)**:
- Now we compute \( b^a = 2^{-1} \).
- By the property of exponents, \( 2^{-1} = \frac{1}{2} \) (because a negative exponent indicates the reciprocal).

4. **Combine the results**:
- Now we multiply the results from the previous steps:
\[ a^b \times b^a = 1 \times \frac{1}{2} = \frac{1}{2}. \]

5. **Final answer**:
- Therefore, the value of \( a^b \times b^a \) is \( \frac{1}{2} \).