Question

How do you simplify `.(a/b^3)^-3`?

Answer 1

Have a look:

Explanation:

You can consider that your negative cube is going to be applied to both numerator and denominator.
So you get:

`(a/b^3)^-3=((a)^-3)/((b^3)^-3)=`
you now use the rule of exponents where `(x^a)^b=x^(a*b)` to get:
`a^-3/(b^-9)`

At this point you can use (although I am not sure about the usefulness of it) the idea that a negative exponent sends your base to another "floor"; so if, say, `a` is at the numerator it can go downstairs to the denominator and viceversa.
In your case you can write:
`a^-3/(b^-9)=b^9/a^3`