80 x 100 = 8000
80 times 100 is 8000. Strip the zeros first: 8 x 1 = 8, then put all three zeros back. The answer is a perfect cube, because 20 x 20 x 20 also equals 8000.
80 × 100 = 8,000
Adding 80 to itself 100 times gives the same answer.
Zeros out, zeros back in
80 carries one zero and 100 carries two. Multiply the leading digits, 8 x 1 = 8, then reattach all three zeros to get 8000. Counting the zeros before you start is faster than lining the numbers up in columns, and it cannot go wrong so long as you count every one of them.
8000 is a cube
20 x 20 x 20 = 8000, so the cube root of 8000 is exactly 20. Of all the four-digit numbers that end in three zeros, only 1000 and 8000 are perfect cubes, which makes 8000 worth recognising on sight.
Doubling from a smaller pair
80 is double 40, so 8000 is double 40 x 100 = 4000. Halve it twice and you are at 2000. Going the other direction, 8 x 100 = 800 is this same answer with one zero taken off.