Find the tens place of the number 7281×3264.

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Question

Find the tens place of the number $7^{281} \times 3^{264}$ .

Options:

A . 2

B . 4

C . 6

D . 8

Answer: Option C
:
C

To find the tens place, we need to find the remainder when this number is divided by 100.
$\frac{7^{281}}{100} ∣ r$ $= \frac{((7^{4})^{70} \times 7^{1})}{100} ∣ r$ $= \frac{((. .49 \times . .49)^{70} \times 7^{1})}{100} ∣ r = \frac{((. .01)^{70} \times 07)}{100} ∣ r = . .07$
Similarly, $\frac{3^{264}}{100} ∣ r$ $= \frac{(3^{4})^{66}}{100} ∣ r$ $= \frac{(3^{2} \times 3^{2})^{66}}{100} ∣ r$ $= \frac{(09 \times 09)^{66}}{100} ∣ r$ $= \frac{81^{66}}{100} ∣ r = . .81$
(66 is of the form 5n+1, and the tens digit of $81^{n}$ repeats after a cycle of 5)

Answer is the tens digit of $07 \times 81 = . .6 .$

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