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  • The last digit in <img alt="7^{300}" src="https://entrancecorner.oncodecogs.com/gif.latex?7%5

The last digit in 7^{300} is

Option: 1

7


Option: 2

9


Option: 3

1


Option: 4

3


Answers (1)

best_answer

We have 7^2=49=50-1

Now  7^{300}=\left(7^2\right)^{150}=(50-1)^{150}

\begin{aligned} & ={ }^{150} C_0(50)^{150}(-1)^0+{ }^{150} C_1(50)^{149}(-1)^1+\ldots \ldots +{ }^{150} C_{150}(50)^0(-1)^{150} \\ & \end{aligned}Thus the last digits of 7^{300} are  { }^{150} C_{150} \cdot 1.1  i.e., 1

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shivangi.shekhar

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