Final answer:
To find the remainder when 5^400 is divided by 19, divide the exponent (400) by 18 to find a quotient of 22 and a remainder of 4. Therefore, the remainder is 4.
Step-by-step explanation:
To find the remainder when 5400 is divided by 19, we can use the concept of modular arithmetic.
We start by computing the remainders of 5 raised to the powers of 1, 2, 3, 4, and so on, until we spot a pattern.
We notice that the remainders repeat every 18 powers of 5. Therefore, to find the remainder when 5400 is divided by 19, we divide the exponent (400) by 18 to get a quotient of 22 and a remainder of 4.
So, the remainder when 5400 is divided by 19 is 4.