The PowerShell script below extracts one file from zip-archive which contains several files. I use code like this to get files with financial references from zip-archives and update SharePoint lists from them. So there's a lot of things where this sctipt can be used.

Below I write a sctipt with comments. So I don't think it would be difficult to understand the meaning of code.

function ExtractFilesFromZip($zipsource, $filename, $dest) { 


        foreach($item in $zipsource.items()) { 
                If ($item.Name -eq $filename) { 
                        $shell.NameSpace($path).copyhere($item, $FOF_SILENT_FLAG + $FOF_NOCONFIRMATION_FLAG) 
                else {
                        # you can add something for logging or debugging

#connect shell.application to work with zipped content
$shell = new-object -com shell.application 

#path where zip-archive is
$path = "C:\DataFolder\Work\"

#filename of archive
$zip_file = "" 

#name of file for extracting 
$file_to_extract = "eas029.csv" 

#read zip content 
$zip = $shell.NameSpace($path + $zip_file) 

#execute function
ExtractFilesFromZip -zipsource $zip -filename $file_to_extract -dest $path