id,node_id,number,title,user,state,locked,assignee,milestone,comments,created_at,updated_at,closed_at,author_association,active_lock_reason,draft,pull_request,body,reactions,performed_via_github_app,state_reason,repo,type
1188406993,I_kwDOAMm_X85G1abR,6430,Bug in broadcasting with multi-indexes,2448579,closed,0,,,1,2022-03-31T17:25:57Z,2022-04-13T14:49:23Z,2022-04-13T14:49:23Z,MEMBER,,,,"### What happened?

``` python
import numpy as np
import xarray as xr

ds = xr.Dataset(
    {""foo"": ((""x"", ""y"", ""z""), np.ones((3, 4, 2)))},
    {""x"": [""a"", ""b"", ""c""], ""y"": [1, 2, 3, 4]},
)
expected = ds.sum(""z"")
stacked = ds.stack(space=[""x"", ""y""])

broadcasted, _ = xr.broadcast(stacked, stacked.space)

stacked.sum(""z"").unstack(""space"")  # works
broadcasted.sum(""z"").unstack(""space"")  # error
```

```
---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Input In [13], in <module>
     10 broadcasted, _ = xr.broadcast(stacked, stacked.space)
     11 stacked.sum(""z"").unstack(""space"")
---> 12 broadcasted.sum(""z"").unstack(""space"")

File ~/work/python/xarray/xarray/core/dataset.py:4332, in Dataset.unstack(self, dim, fill_value, sparse)
   4330     non_multi_dims = set(dims) - set(stacked_indexes)
   4331     if non_multi_dims:
-> 4332         raise ValueError(
   4333             ""cannot unstack dimensions that do not ""
   4334             f""have exactly one multi-index: {tuple(non_multi_dims)}""
   4335         )
   4337 result = self.copy(deep=False)
   4339 # we want to avoid allocating an object-dtype ndarray for a MultiIndex,
   4340 # so we can't just access self.variables[v].data for every variable.
   4341 # We only check the non-index variables.
   4342 # https://github.com/pydata/xarray/issues/5902

ValueError: cannot unstack dimensions that do not have exactly one multi-index: ('space',)
```

### What did you expect to happen?

This should work.

### Minimal Complete Verifiable Example

_No response_

### Relevant log output

_No response_

### Anything else we need to know?

_No response_

### Environment

xarray main after the flexible indexes refactor","{""url"": ""https://api.github.com/repos/pydata/xarray/issues/6430/reactions"", ""total_count"": 0, ""+1"": 0, ""-1"": 0, ""laugh"": 0, ""hooray"": 0, ""confused"": 0, ""heart"": 0, ""rocket"": 0, ""eyes"": 0}",,completed,13221727,issue