1. You have the following expression: (8r^-5)^-3
2. Keepin on mind the exponents properties, you must multiply the exponent (-5) by the exponent (-3), and the exponent 1 by the exponent (-3),as below:
(8r^-5)^-3
(8^(1)(-3))(r^(-5)(-3 ))
(8^-3)(r^15)
3. The negative exponent indicates that the base 8 must be in the denominator. Therefore, you have:
r^15/8^3
r^15/512
4. The simplified form of (8r^-5)^-3 is:
r^15/512