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Q. The last digit in $7^{300}$ is

Binomial Theorem

Solution:

$7^{300}= \left(7^2\right)^{150}=(50-1)^{150} $
$={ }^{150} C_0(50)^{150}(-1)^0+{ }^{150} C_1(50)^{149}(-1)^1 $
$+\ldots+{ }^{150} C_{150}(50)^{\circ}(-1)^{150}$
Thus, the last digit of $7^{300}$ is ${ }^{150} C _{150} \cdot 1 \cdot 1=1$