recently, i've started to learn more about GI and the techniques that we can use to implement.

one of the main basic things that i've learned in this topic is Radiance and Irradiance.

Radiance is the spatial density of radiation incident at a surface, regardless of the direction

and Irrediance is the same thing but with direction and orientation dependency.

in Irradiance the numerator is d?(p)

but in Radiance, the numerator is d^2?(p,w)

so my question is why the power of Radiance's derivative is 2 ?

Because radiance is flux differentiated with respect to two quantities (projected solid angle and surface area) which gives you two differential operators in the denominator and therefore two in the numerator as well. Radiometry isn't really that hard once you got it but it can take some time and practice(!) depending on your foreknowledge and basic intelligence. :)