Anonymous

(3^4)^175=81^175 a number ending with 1,when repeatedly multiplied with itself will yield a number ending with 1 in the units place.

Anonymous

3² = 9 3² ≡ -1 (mod 10) 3⁷⁰⁰ ≡ (3²)³⁵⁰ 3⁷⁰⁰ ≡ (-1)³⁵⁰ 3⁷⁰⁰ ≡ 1 (mod 10) When divided by 10, 3⁷⁰⁰ leaves remainder 1. Therefore, 1 is the units digit of 3⁷⁰⁰.

Anonymous

The units digit of 3^700 is 1.

Anonymous

3^0 ---> 1 3^1 ---> 3 3^2 ---> 9 3^3 ---> 7 3^4 ---> 1 3^5 ---> 3... See the pattern? The units digit repeats every 4 powers of 3. Since 700 is a number divisible by 4, the units digit is the same as that of 3^0 and 3^4 -- 1. That's your answer.

Anonymous

Notice that 3^4 = 81 with a last digit of 1. Next notice that: 81 * 81 * 81 * ... --> the result will always have a last digit of 1. So just rewrite 3^700 as follows: 3^700 = 3^(4 * 175) = (3^4)^175 = 81^175 The last digit is 1.

Anonymous

3^1 = 3 3^2 = 9 3^3 = 27 =>> 7 3^4 = 81 =>> 1 3^5 = 243 =>> 3 3^6 = 729 =>> 9 3^7 = 2187 =>> 7 3^8 = 6561 =>> 1 So we see that 3^(4n) ends with 1 3^(4n + 1) ends with 3 3^(4n + 2) ends with 9 3^(4n + 3) ends with 7 3^700 => 3^(4 * 175) It ends with 1