Here's why:
* Absolute Magnitude (M): This measures a star's intrinsic brightness as if it were located 10 parsecs away from Earth.
* Apparent Magnitude (m): This measures how bright a star appears from Earth.
The relationship between apparent magnitude (m), absolute magnitude (M), and distance (d) is given by the following formula:
```
m - M = 5 * log(d/10)
```
If we set m = M, the formula becomes:
```
0 = 5 * log(d/10)
```
Solving for d, we get:
```
d = 10 parsecs
```
Therefore, at a distance of 10 parsecs, the apparent magnitude and absolute magnitude of a star would be identical. This is because the apparent brightness would be exactly the same as its intrinsic brightness at that specific distance.
