Find the ten’s digit of 74288

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Question

Find the ten’s digit of $74^{288}$

Options:

A . 3

B . 6

C . 7

D . 8

Answer: Option C
:
C

Ans. (c)

$74^{288} = (37 \times 2)^{288}$ (refer demo tutorial for last 2 digits technique)

$37^{288} \times 2^{288}$

$(37^{4})^{72} \times (2)^{288}$

$(37^{2} \times 37^{2})^{72} \times (__56)$

$(69 \times 69)^{72} \times (__56)$

$(__61)^{72} \times (__56)$

$(__21) \times (__56) =__76.$ answer is 7

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