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

Answer

To solve the expression \( a^b - b^a \) given \( a = -1 \) and \( b = 2 \), we will follow these steps:

### Step 1: Substitute the values of \( a \) and \( b \)

We have:
- \( a = -1 \)
- \( b = 2 \)

Substituting these values into the expression gives us:
\[ (-1)^2 - 2^{-1} \]

### Step 2: Calculate \( (-1)^2 \)

Now, we calculate \( (-1)^2 \):
\[ (-1)^2 = 1 \]

### Step 3: Calculate \( 2^{-1} \)

Next, we calculate \( 2^{-1} \):
\[ 2^{-1} = \frac{1}{2} \]

### Step 4: Substitute the results back into the expression

Now we substitute the results back into the expression:
\[ 1 - \frac{1}{2} \]

### Step 5: Simplify the expression

To simplify \( 1 - \frac{1}{2} \), we can convert \( 1 \) into a fraction:
\[ 1 = \frac{2}{2} \]
So,
\[ \frac{2}{2} - \frac{1}{2} = \frac{2 - 1}{2} = \frac{1}{2} \]

### Final Answer

Thus, the value of \( a^b - b^a \) is:
\[ \frac{1}{2} \]

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