I. Mrs. Luisa asks for a quote to repair eight pieces of jewelry. The jewelry store manager tells him that he will charge $6 for the first piece of jewelry, and for each successive piece three times as much as the previous one. How much will the jeweler charge Mrs. Luisa?

Let's calculate the total cost for each piece of jewelry:

For the first piece: $6
For the second piece: $6 x 3 = $18
For the third piece: $18 x 3 = $54
For the fourth piece: $54 x 3 = $162
For the fifth piece: $162 x 3 = $486
For the sixth piece: $486 x 3 = $1458
For the seventh piece: $1458 x 3 = $4374
For the eighth piece: $4374 x 3 = $13122

Now, let's sum up the costs for all eight pieces of jewelry:
$6 + $18 + $54 + $162 + $486 + $1458 + $4374 + $13122 = $19620

Therefore, the jeweler will charge Mrs. Luisa a total of $\$19620$ for repairing eight pieces of jewelry.

\boxed{\$19620}