last-digit-of-a-large-number

Last digit of a large number

Define a function that takes in two non-negative integers $a$ and $b$ and returns the last decimal digit of $a^b$. Note that $a$ and $b$ may be very large!

For example, the last decimal digit of $9^7$ is $9$, since $9^7 = 4782969$. The last decimal digit of $({2^{200}})^{2^{300}}$, which has over $10^{92}$ decimal digits, is $6$. Also, please take $0^0$ to be $1$.

You may assume that the input will always be valid.

Examples

lastDigit(new BigInteger("4"), new BigInteger("1")) // returns 4
lastDigit(new BigInteger("4"), new BigInteger("2")) // returns 6
lastDigit(new BigInteger("9"), new BigInteger("7")) // returns 9
lastDigit(new BigInteger("10"), new BigInteger("10000000000")) // returns 0