I bring the r^2 up to the top, where it becomes r^-2. I then would tell the student to add the exponents where the base is the same. I think I interpreted the equation differently here, making t part of the exponent.
So, combining the constants, we have [-1/2r^(8t-2)]^3
We cube each factor. That means, in the case of the exponent, multiplying it by 3. One is left with:
= -1/16r^(24t - 6)
Did I do something amiss?
Students should not just be told the laws of exponents. Rather, they should be led through an investigation of how one might assign values to exponents such as zero, 1, negative values, fractional values, and irrational values. It turns out that many students really do not like being "told" what the rules are, but like having it explained why those are the rules. They really do appreciate the more in depth explanation.