Using ADK for Windows 8.1, and the DISM cmdlets that come with them. I have WMF 4.0 installed. My machine is Windows 7 x64 SP1, and I'm trying to mount the wim using

PS C:\Users\BigHomie> Mount-WindowsImage -ImagePath 'C:\Program Files (x86)\Windows
Kits\8.1\Assessment and Deployment Kit\Windows Preinstallation Environment\x86\
en-us\winpe.wim' -Path C:\WinPE_x86 -index 1

And receive the following error:

Mount-WindowsImage : DismInitialize failed. Error code = 0x8007007e
At line:1 char:1
+ Mount-WindowsImage -ImagePath 'C:\Program Files (x86)\Windows
Kits\8.1\Assessmen ...
+ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~~~
    + CategoryInfo          : NotSpecified: (:) [Mount-WindowsImage], COMExcep
   tion
    + FullyQualifiedErrorId : Microsoft.Dism.Commands.MountWindowsImageCommand

Using dism.exe works fine.

Update

Forgetting I had this problem, I went to mount a wim using the Powershell ISE and actuallygot a visual error message about

"C:\Program Files (x86)\Windows Kits\8.1\Assessment and Deployment Kit\Deployment Tools\x86\DISM\api-ms-win-downlevel-advapi32-l4-1-0.dll" 

not being installed. After checking that the dll did in fact exist in the folder I called regsvr32 and received another error message

Will try reinstalling as recommended.