My external hard drive is corrupt and can't repair and format it, what to do?

As you said the drive dropped while backing up, such sudden power outage and ejection may damage the drive's file system, partition table, etc., causing the drive unreadable by your Mac. If you don't need to get off files from the drive, you can directly format the corrupted drive to make it works again.

In case there are any important files kept on the corrupted drive, you'd better recover data from it with data recovery software such as iBoysoft Data Recovery for Mac in advance, or you can restore it from your backups later. To fix corrupted external hard drive on Mac, you can try these methods:

Repair the drive with Disk Utility's First Aid. If Disk Utility can't repair disks, you can try the FSCK command in Single User Mode.

Reformat the drive to eliminate logical errors on the drive. If you can't format the drive, try to erase selected volumes, erase the drive via Terminal commands, format it in Recovery Mode, and enter Safe Mode.

Unluckily, all methods above fail to fix the corrupted external drive on Mac, the drive may be physically damaged, then you can take it to a local repair for further help or consider a replacement.