Approximate the area under the curve $y=\frac{1}{\sqrt[\phantom{2}]{x-2}}$ from $x=3$ to $x=9$ using left and right approximations with $6$ subintervals. Provide both the exact and rounded answers for each.

a$)$ Left Approximation exact answer: $$

b$)$ Left Approximation rounded to the nearest hundredth: $$

c$)$ Right Approximation exact answer: $$

d$)$ Right Approximation rounded to the nearest hundredth: $$