What is the units digit of \(17^{27}\)?When we need to find units digit of any power then units digit is same as the units digit of the base raised to the exponent.=> Units digit of \(17^{27}\) = Units digit of \(7^{27}\)
Now to find the unit's digit of \(7^{27}\), we need to find the pattern / cycle of unit's digit of power of 7 and then generalizing it.
Unit's digit of \(7^1\) = 7
Unit's digit of \(7^2\) = 9
Unit's digit of \(7^3\) = 3
Unit's digit of \(7^4\) = 1
Unit's digit of \(7^5\) = 7
So, unit's digit of power of 7 repeats after every \(4^{th}\) number.
=> We need to divided 27 by 4 and check what is the remainder
=> 27 divided by 4 gives 3 remainder
=> \(7^{27}\) will have the same unit's digit as \(7^3\)
=> Unit's digits of \(7^{27}\) = 3
So,
Answer will be CHope it helps!
Link to Theory for Last Two digits of exponents here.Link to Theory for Units' digit of exponents here.