If `x^(**)y` represents the number of integers between x and y, then `(-2^(**) 8) + (2^(**) - 8) = `

Options

A. 0
B. 9
C. 10
D. 18

Answer

To solve the problem, we need to evaluate the expression `(-2^(**) 8) + (2^(**) -8)` where `x^(**)y` represents the number of integers between `x` and `y`.

### Step-by-Step Solution:

1. **Evaluate `-2^(**) 8`:**
- We need to find the number of integers between `-2` and `8`.
- The integers between `-2` and `8` are: `-1, 0, 1, 2, 3, 4, 5, 6, 7`.
- Count these integers:
- From `-1` to `7`, we have a total of `9` integers.
- Therefore, `-2^(**) 8 = 9`.

2. **Evaluate `2^(**) -8`:**
- Now we need to find the number of integers between `-8` and `2`.
- The integers between `-8` and `2` are: `-7, -6, -5, -4, -3, -2, -1, 0, 1`.
- Count these integers:
- From `-7` to `1`, we have a total of `9` integers.
- Therefore, `2^(**) -8 = 9`.

3. **Add the results:**
- Now we add the results from the two evaluations:
- `(-2^(**) 8) + (2^(**) -8) = 9 + 9 = 18`.

### Final Answer:
Thus, the final answer is `18`.

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