To simplify this expression, let's first rewrite the mixed number as an improper fraction:

2 7/9 = (2*9 + 7)/9 = 25/9

Now, substitute this back into the original expression:

(25/9)^9 * 3^19/5^15

Next, we can simplify the exponents by multiplying:

(25^9 / 9^9) * 3^19 / 5^15

Now, let's calculate the values of the individual terms:

25^9 = 1953125
9^9 = 387420489
3^19 = 1162261467
5^15 = 30517578125

Finally, plug these values back into the expression:

(1953125 / 387420489) * 1162261467 / 30517578125

Now, multiply the fractions:

(1953125 1162261467) / (387420489 30517578125)

Calculating the numerator and denominator separately:

Numerator = 2264838399062500
Denominator = 1180240701025396754282126875

Therefore, the final simplified value of the expression is:

2264838399062500 / 1180240701025396754282126875 = 0.00191733 (approx)