Before powering down any attached USB storage device click on the "Safely Remove Hardware" icon in the right-hand tray of your Windows PC, then click on the device in question and click "Stop".
Once the operating system says it is safe to remove the storage device THEN power it down.
When re-attaching to another device, or when powering up in general, I like to attach the storage device first THEN power it up. There are those that say you should apply power first to get the disk spinning then attach via USB. I really don't think there is any difference. I like my way because then I can attach the external HDD and just forget about it, and turn it on when needed, and turn it off when no longer needed (after stopping as described above) and not worry about the USB cable attach, detach.
TJR