The Units Are Always Important

81 x 82 x 83..... x 98 x 99

This sequence has the number 90 in it.

Therefore it will have the digit 0 in it's unit's place.

The unit's digit is the unit's digit of $1\times2\times3\times4\times5\times6\times7\times8\times9$ . Since, $2\times5$ are included as factors, the unit's digit must be $0$ because $2\times5=10$ and any number multiplied by $0$ is $0$ .

Let the sequence be the product of 19 numbers. Then the product of this 19 numbers' unit digit will be

1 2 3....... 9 But after 1 2 3 4 the answer is 24 and 24*5(next number) is 120... Now on reaching 120 we have 0 as the unit digit so all other numbers will give product equal to 0