Powershell: SharePoint 2013 Create Web Application, Root Site Collection,

host-named-sites.ps1

# Replace:
#   DATABASE
#   NAMED
#   APPLICATION NAME
#   hostheadername
#   DOMAIN\USER
#   DOMAIN\SP_FARM_ACCOUNT
#   PATHNAME
#   SITE COLLECTION NAME
#   DIRECTORYPORT

# Create Authentication Provider
$ap = New-SPAuthenticationProvider

# Create Web Application
$w = New-SPWebApplication -DatabaseName "WSS_Content_DATABASE" -ApplicationPool "NAMED App Pool" -Name "APPLICATION NAME" -Port 80 -AuthenticationProvider $ap1 -ApplicationPoolAccount (Get-SPManagedAccount 'DOMAIN\SP_FARM_ACCOUNT') -Path "%wwwroot%\wss\VirtualDirectories\DIRECTORYPORT" -HostHeader "hostheadername"
iisreset /noforce

# Create Root Site Collection
$w = Get-SPWebApplication "APPLICATION NAME"
New-SPSite http://sub.domain.com -OwnerAlias "DOMAIN\USER" -HostHeaderWebApplication $w -Name "APPLICATION NAME" -Template "BLANKINTERNETCONTAINER#0"

# Create Managed Path Site Collection
New-SPManagedPath "PATHNAME" -HostHeader -Explicit
New-SPSite http://sub.domain.com/PATHNAME -OwnerAlias "DOMAIN\USER" -HostHeaderWebApplication $w -Name "SITE COLLECTION NAME" -Template "BLANKINTERNETCONTAINER#0"