How can I exit Microsoft GW-BASIC, IBM BASICA, or other similar old dialects of BASIC?

GWBASIC and its clones (e.g., IBM's BASIC and BASICA) exited to the DOS prompt with the command system.

Although redirection was possible even in early versions of MS-DOS/PC-DOS, the BASIC interpreter bypassed using the standard input and output streams, and had its own Ctrl-Break/Ctrl-C handler, so neither of those keystrokes would terminate the interpreter.
The shell command started a fresh copy of the system command interpreter (usually COMMAND.COM), or executed a system command and then returned to BASIC, but did not remove the interpreter from memory.

Type "system" and hit enter to exit GW-BASIC in DOS.

Type "shell" and hit enter to go to DOS but still have GW-BASIC in memory. Type "exit" while in DOS to return to GW-BASIC.