If `a=(-1)^(2009)` and `b=(-1)^(2010)`, then find the value of ab.

Options

A. 1
B. `-1`
C. 2009
D. 2010

Answer

To find the value of \( ab \) where \( a = (-1)^{2009} \) and \( b = (-1)^{2010} \), we can follow these steps:

### Step 1: Calculate \( a \)
We start by calculating \( a \):
\[ a = (-1)^{2009} \]
Since 2009 is an odd number, we know that:
\[ (-1)^{\text{odd}} = -1 \]
Thus,
\[ a = -1 \]

### Step 2: Calculate \( b \)
Next, we calculate \( b \):
\[ b = (-1)^{2010} \]
Since 2010 is an even number, we know that:
\[ (-1)^{\text{even}} = 1 \]
Thus,
\[ b = 1 \]

### Step 3: Calculate \( ab \)
Now we can find \( ab \):
\[ ab = a \times b = (-1) \times 1 \]
Calculating this gives:
\[ ab = -1 \]

### Final Answer
Thus, the value of \( ab \) is:
\[ \boxed{-1} \]