To simplify this expression, we first need to cancel out common terms in the numerator and denominator.

Given expression: (3p^4/5q^8) * (15q^2(p-5)/7q^6)

Step 1: Simplify each fraction separately.

3p^4 / 5q^8 = (3/5)*(p^4/q^8)

15q^2(p-5) / 7q^6 = (15/7)[(q^2)(p-5)/q^6]

Step 2: Combine the simplified fractions.

(3/5)(p^4/q^8) (15/7)[(q^2)(p-5)/q^6]

Step 3: Multiply the numerators and denominators.

[(315p^4q^2(p-5)) / (57q^8*q^6)]

Step 4: Simplify the expression.

(45p^4q^2(p-5)) / (35q^14)

Therefore, the simplified expression of (3p^4/5q^8) * (15q^2(p-5)/7q^6) is (45p^4q^2(p-5)) / (35q^14).