Discussion

Explanation:

Let us find the pattern that remainders follow when successive powers of 2 are divided by 7.

Remainder of 21/7 = 2.
Remainder of 22/7 = 4.
Remainder of 23/7 = 1.
Remainder of 24/7 = 2.
Remainder of 25/7 = 4.
Remainder of 26/7 = 1.

∴ We find that the remainders are repeated after every three powers. 

R21007 =  R299×217 = R2997×R217 = 1 × 2 = 2

⇒ The remainder is 2.

Hence, 2.

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