The last digit in 7^{300} is | vedclass

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Question

(C) We have $7^2 = 49 = 50 - 1$.Now,$7^{300} = (7^2)^{150} = (50 - 1)^{150}$.Using the binomial expansion,$(50 - 1)^{150} = \sum_{k=0}^{150} \binom{15

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(C) We have $7^2 = 49 = 50 - 1$.Now,$7^{300} = (7^2)^{150} = (50 - 1)^{150}$.Using the binomial expansion,$(50 - 1)^{150} = \sum_{k=0}^{150} \binom{150}{k} (50)^{150-k} (-1)^k$.All terms except the last one contain a factor of $50$,which means they end in $00$ or higher powers of $10$.The last term is $\binom{150}{150} (50)^0 (-1)^{150} = 1 	imes 1 	imes 1 = 1$.Thus,the last digit of $7^{300}$ is $1$.

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

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