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If p=(-1)^(205) and q=(-1)^(202), then p...

If `p=(-1)^(205)` and `q=(-1)^(202)`, then `p+q` is

A

`(-1)^(407)`

B

`(-1)^(4)`

C

`0`

D

`-2`

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to evaluate the expressions for \( p \) and \( q \) and then find \( p + q \). ### Step-by-Step Solution: 1. **Evaluate \( p \)**: \[ p = (-1)^{205} \] Since 205 is an odd number, we use the property that \( (-1)^{\text{odd}} = -1 \). \[ p = -1 \] 2. **Evaluate \( q \)**: \[ q = (-1)^{202} \] Since 202 is an even number, we use the property that \( (-1)^{\text{even}} = 1 \). \[ q = 1 \] 3. **Calculate \( p + q \)**: \[ p + q = -1 + 1 \] Simplifying this gives: \[ p + q = 0 \] ### Final Answer: \[ p + q = 0 \]
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