If we multiply 1 through 10, the mathematical representation of the product would be, P = 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 Getting the factors of each number, P = 1 x 2 x 3 x (2 x 2) x 5 x (3 x 2) x 7 x (2 x 2 x 2) x 9 x (5 x 2) Then, we take out all the 2's. 2 x (2 x 2) x (3 x 2) x (2 x 2 x 2) x (5 x 2) Combining all the 2's. 2^8 x 3 x 5 2^8 can also be written as (2 x 2)^4. Thus, the answer is 4.
Using the rectangular route Mike rides 12 miles. If he rides diagonally the distance is √2²+10²=√4+100=√104. The difference between the two routes is 12-√104=1.80 miles approximately.
