Question

The digit of unit place (623)49

Answer 1

Unit place will have 6 as a digit

Answer 2

Answer:

The unit digit of $623^{49}$ is 3.

Step-by-step explanation:

To find a unit digit exponents, we should consider last digit of the base and then the exponent.

Like here, we should try to find exponent of $3^{49}$. Whatever answer we will get is the unit digit of $623^{49}$.

Let us observe and understand the cycle of exponent of 3.

$3^0 = 1\\3^1 = 3\\3^2 = 9\\3^3 = 27\\3^4 = 81\\3^5 = 243\\3^6 = 729\\3^7 = 2187$

We can observe that 1,3,9 & 7 are the numbers that repeats when we increase the exponent by  1.

Hence we can classify exponent as 4n, 4n+1, 4n+2 & 4n+3 where n is any whole number then the unit digit is 1, 3, 9 & 7 respectively.

For the exponent 49 we can write it as 4(12) + 1 which is of the form 4n+1.

Hence the unit digit of $3^{49}$ & $623^{49}$ is 3.