How to solve a problem like this:

Let $N = 11$. What is $2^{2652557887263} \pmod N$?

As part of the questions we are given the multiplication table for $\mathbb{Z}\_{11}$:

```
x | 1  2  3  4  5  6  7  8  9  10
---------------------------------
1 | 1  2  3  4  5  6  7  8  9 10
2 | 2  4  6  8 10  1  3  5  7  9
3 | 3  6  9  1  4  7 10  2  5  8
4 | 4  8  1  5  9  2  6 10  3  7
5 | 5 10  4  9  3  8  2  7  1  6
6 | 6  1  7  2  8  3  9  4 10  5
7 | 7  3 10  6  2  9  5  1  8  4
8 | 8  5  2 10  7  4  1  9  6  3
9 | 9  7  5  3  1 10  8  6  4  2
10|10  9  8  7  6  5  4  3  2  1

```

...as well as $(\mathbb{Z}\_{11}^\*,\times)$, the group of units of $\mathbb{Z}\_{11}$ under multiplication:

```
exp|  0   1   2   3   4   5   6   7   8   9   10
 ------------------------------------------------
 g | g^0 g^1 g^2 g^3 g^4 g^5 g^6 g^7 g^8 g^9 g^10
 ------------------------------------------------
 1 |  1   1   1   1   1   1   1   1   1   1   1
 2 |  1   2   4   8   5  10   9   7   3   6   1
 3 |  1   3   9   5   4   1   3   9   5   4   1
 4 |  1   4   5   9   3   1   4   5   9   3   1
 5 |  1   5   3   4   9   1   5   3   4   9   1
 6 |  1   6   3   7   9  10   5   8   4   2   1
 7 |  1   7   5   2   3  10   4   6   9   8   1
 . |
 10|  1  10   1  10   1  10   1  10   1  10   1

```

Overall, I'm having trouble understanding **how the numbers in the table are generated, and how they're used to solve the aforementioned question**.