If $17^{200}$ is divided by 18, the remainder is

Using modular arithmetic, we need to find $17^{200}(\mathrm{mod}18)$.
We know that:

$$17\equiv -1(\mathrm{mod}18)$$

Therefore:

$$17^{200}\equiv (-1{)}^{200}(\mathrm{mod}18)$$

Since the exponent $200$ is an even number:

$$(-1{)}^{200}=1$$

Thus, the remainder when $17^{200}$ is divided by 18 is $1$.