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)
 
 (a ^ 9) (b ^ 6)