Dividing by 5 is the same as multiplying by 10 and dividing by 2. Multiplying by 10 just moves the decimal point over one place. Dividing by 2
7^1 = 7 ÷ 5 = 1.4 7^5 = 16807 ÷ 3361.4
7^2 = 49 ÷ 5 = 9.8 7^6 = 117649 = 23529.8
7^3 = 343 ÷ 5 = 68.6 etc.
7^4 = 2401 ÷ 5 = 480.2
This pattern cycles every 4 numbers. Which row will 7^2014 be in?
Working with the exponents: 1 ÷ 4 = .25 5 ÷ 4 = 1.25
2 ÷ 4 = .50 6 ÷ 4 = 1.50
3 ÷ 4 = .75 7 ÷ 4 = 1.75
4 ÷ 4 = 1.00 8 ÷ 4 = 2.00
2014 ÷ 4 = 503.5 ---> second row
Therefore, from the top grouping, the decimal is .8 ---> remainder is 5 x .8 = 4
im 10 and in 6 im a little young for my grades
