Step 1: Find remainder of powers of 9 when divided by 6.

$9 \equiv 3$ (Reminder) (When divided by 6) Therefore, any power of 9 will have the same remainder as the corresponding power of 3 when divided by 6.

Compute: $3^1 \equiv 3$ (Reminder When divided by 6) $3^2 \equiv 3$ (Reminder When divided by 6)
$3^3 \equiv 3$ (Reminder When divided by 6) ... Thus, for all $n \geq 1$, $3^n \equiv 3$ (Reminder When divided by 6)

Hence, each term $9^3$, $9^4$, $9^5$, …, $9^{100}$ leaves remainder 3 when divided by 6.

Step 2: Count number of terms. From $9^3$ to $9^{100}$ → Number of terms = $100 - 3 + 1 = 98$ terms.

Step 3: Find remainder of the total sum.

Each term contributes remainder 3, so total remainder = $(98 \times 3) \div 6$

$= 294 \div 6 = 49$, which is an integer.

Hence, final remainder = 0