To find the reciprocal of a number, we simply take the inverse of that number.

First, let’s simplify the expression inside the absolute value:

-(17/81) × (-5/34) × (-9/5)

Multiplying the fractions, we get:

(17/81) × (5/34) × (9/5)

Now, let’s simplify further:

(17 × 5 × 9) / (81 × 34 × 5)

765 / 13770

Now, to find the reciprocal, we take the inverse of this fraction:

Reciprocal = 1 / (765 / 13770)

To divide by a fraction, we multiply by its reciprocal:

Reciprocal = 1 × (13770 / 765)

Reciprocal = 13770 / 765

Therefore, the reciprocal of

-(17/81) × (-5/34) × (-9/5)

is 13770/765.