First, a correction: it's Memphis, Tennessee (not "mephis"). The driving distance to Miami, Florida is approximately 1,100 miles (1,770 km).
I-40 E (Memphis) → I-55 S (to I-10 E) or I-22 E → I-65 S → I-10 E → I-75 S (Florida Turnpike) → Miami.
Common path: Memphis → Birmingham → Mobile → Tallahassee → Lake City → Orlando → Fort Lauderdale → Miami.
MEM → MIA: 2h 15m nonstop (American, Frontier). Often <$200 roundtrip if booked ahead.