Would (6^3)^-3 cancel out to just 6? or it will be 6^0?

The rule for an exponent raised to another exponent is:

(a^b)^c is equal to a^(b*c) so in this case:

(6^3)^(-3) is equal to:

6^(-9)  which is

1/(6^9) which is:

1/10077696

What you described is what happens when you multiply two similar bases with exponents, for example

(a^b)(a^c)=a^(b+c) so if your problem was:

(6^3)(6^-3) then yes it would be equal to:

6^(3-3)

6^0

1

So keep those rules in mind...

(a^b)(a^c)=a^(b+c)

and

(a^b)^c=a^(b*c)