Question

If x + y = 11, then $(-1)^x + (-1)^y$ is equal to _____

(where x, y are whole numbers).

• A. 2
• B. 1
• C. 0
• D. -1

Answer 1

Answer:

C. 0

The value of (-1) raised to a power depends on whether the power is even or odd:

• If the power is even, $(-1)^{even} = 1$

• If the power is odd, $(-1)^{odd} = -1$

We know that x + y = 11, which is an odd number.

For the sum of two whole numbers to be odd, one of the numbers must be even, and the other must be odd.

Therefore, we have two possibilities:

1. x is even, y is odd:

   • $(-1)^x = 1$

   • $(-1)^y = -1$

   • $(-1)^x + (-1)^y = 1 + (-1) = 0$

2. x is odd, y is even:

   • $(-1)^x = -1$

   • $(-1)^y = 1$

   • $(-1)^x + (-1)^y = -1 + 1 = 0$

In both cases, the result is 0.

Therefore, $(-1)^x + (-1)^y = 0$.