This is because ABE is a right triangle with the right angle being angle BAE. We know that AB = 8 and EB = 10, so we can use the Pythagorean Thoerem to find AE.
If it is to the negative power, you live the decimal point to the left (if positive, move to the right). In the case we move the decimal point 5 places to the left of 7. This results in .00007.