The tens digit of 617 is -

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Question

The tens digit of $6^{17}$ is -

Options:

A . 1

B . 3

C . 5

D . 7

Answer: Option B
:
B

We can use the last two digits technique to solve this question.

$6^{17} = 3^{17} \times 2^{17}$
$3^{17} = (3^{4})^{4} \times 3 = (3^{2} \times 3^{2})^{4} \times 3 = (09 \times 09)^{4} \times 3 = 81^{4} \times 3 = 21 \times 3 = 63$
$2^{17} = (2^{10})^{1} \times 2^{7} = 24 \times . . . . . .28 = . . . . .72$
Answer is the tens digit of the product of 72 and 63 = ...36.

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