Which expression is equivalent to (a - ^8 b/a - ^5 b^3) - ^3? Assume a~0, b~0.

For this case we have the following expression:

(a ^ - 8b / a ^ - 5b ^ 3) ^ - 3

For power properties we have:

((a ^ ( - 8 - ( - 5))) (b ^ (1-3))) ^ - 3

Rewriting we have:

((a ^ ( - 8 + 5)) (b ^ ( - 2))) ^ - 3

((a ^ ( - 3)) (b ^ ( - 2))) ^ - 3

For power properties we have

(a ^ 9) (b ^ 6)

Answer:

(a ^ 9) (b ^ 6)