Question

Question 128(ii)

$\begin{array}{ccccccccccc}X& 1^x& 2^x& 3^x& 4^x& 5^x& 6^x& 7^x& 8^x& 9^x& {10}^x\\ 1& 1& 2& & & & & & & & \\ 2& 1& 4& & & & & & & & \\ 3& 1& 8& & & & & & & & \\ 4& 1& 16& & & & & & & & \\ 5& 1& 32& & & & & & & & \\ 6& 1& 64& & & & & & & & \\ 7& 1& 128& & & & & & & & \\ 8& 1& 256& & & & & & & & \\ \text{Ones digits of the powers}& 1& 2,4,6,8& & & & & & & & \end{array}$
Predict the ones gigit in the following.
$\left(i\right)4^{12}$
$\left(ii\right)9^{20}$
$\left(iii\right)3^{17}$
$\left(iv\right)5^{100}$
$\left(v\right){10}^{500}$

Answer 1

$\text{(i)Ones digit in}{4}^{12}\text{is 6}$
$\text{(ii)Ones digit in}{9}^{20}\text{is 1}$
$\text{(iii)Ones digit in}{3}^{17}\text{is 3}$
$\text{(iv)Ones digit in}{5}^{100}\text{is 5}$
$\text{(v)Ones digit in}{10}^{500}\text{is 0}$