Answer:
b^(10/3)/a^3
Explanation:
Two rules of exponents are involved:
... a^-b = 1/a^b
... (a^b)^c = a^(bc)
Here, this means we can rewrite the given expression as ...
... (a^(4/5)/b^(8/9))^(-15/4) = a^(4/5·(-15/4))/b^(8/9·(-15/4)) . . . . . multiply outer exponent by inner exponents per 2nd rule
... = a^-3/b^(-10/3) . . . . simplify the exponents
... = b^(10/3)/a^3 . . . . . swap numerator and denominator and change exponent signs per 1st rule