Use the negative exponent rules to simplify.
r^-2/r^-6
To simplify this expression using the negative exponent rules, we can apply the rule that states "When a negative exponent is in the numerator, move it to the denominator and change the sign from negative to positive."
Using this rule, we can rewrite the expression as:
r^-2/r^-6 = 1/ (r^2/r^6)
Next, we apply the rule that states "When dividing powers of the same base, subtract the exponents."
Applying this rule, we can simplify the expression further:
1/ (r^2/r^6) = 1/ (r^(2-6)) = 1/ r^(-4)
Finally, using the negative exponent rule again, we move the negative exponent from the denominator to the numerator and change the sign from negative to positive:
1/ r^(-4) = r^4
Therefore, the simplified expression is r^4.