8,9,10  How many integers exist from 1 to 1000000 that are neither perfect squares, nor perfect cubes, nor fourth powers?
$1000000=1000^{2}=100^{3}=10^{6}$. Therefore, in the specified range, there are exactly 1000 squares and 100 cubes. 10 numbers among them are sixth powers, meaning they are both squares and cubes. All fourth powers are found among the squares. Therefore, the numbers that satisfy the condition are

$1000000-1000-100+10=998910$ numbers.

## Answer

998910 numbers.