First, if you have a negative exponent, you can make it positive by putting it in the denominator of a fraction:
An exponent of 1/2 is the same as square root, so the square root of 9 is 3:
The 8 to the 2/3 power can be rewritten using the power-of-a-power property:
An exponent of 1/3 is the same as cube root, so the cube root of 8 is 2:
EDIT: Sorry pickslides!