Search notes:

powershell.exe

powershell.exe is an (unmanaged) interpreter for the .NET assembly System.Management.Automation.
When powershell.exe is started, it determines the required environment and loads the correct CLR (Common Language Runtime) and (managed) PowerShell host (Microsoft.PowerShell.ConsoleHost.dll) (See this link for more information).

Executing a PowerShell script in a cmd.exe batch file

The following example tries to demonstrate how it is possible to execute a PowerShell «script» in a cmd.exe batch file:
@powershell -command "" ^
                        ^
  $i = 1;               ^
                        ^
  while ($i -le 10) {   ^
    write-output $i;    ^
    $i++;               ^
  }                     ^
                        ^
""
Github repository about-PowerShell, path: /powershell.exe/command/execute-script.bat
A few notes:
Note that it is also possible to execute a PowerShell script with the -f or --file command line option.

See also

(Some interesting) command line options/parameters
This exe is referenced under HKEY_LOCAL_MACHINE\Software\Microsoft\Windows\CurrentVersion\App Paths.

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