I want to know about exponent laws properly. Someone can help me !
Thanking you
Swadesh
The "exponent laws" are:
$\displaystyle (a^x)(a^y)= a^{x+ y}$
and
$\displaystyle (a^x)^y= a^{xy}$.
To see why those are true, notice that $\displaystyle a^3= (a)(a)(a)$ and $\displaystyle a^2= (a)(a)$. Multiplying [tex]a^3a^2= [(a)(a)(a)][(a)(a)]= (a)(a)(a)(a)(a)= a^5= a^{2+ 3}[tex] and
$\displaystyle (a^2)^3= (a^2)(a^2)(a^2)= ((a)(a))((a)(a))((a)(a))= a^6= a^{2(3)}$
You sure?!
https://www.google.ca/?gws_rd=ssl#q=0%5E0%3D
last paragraph by the "mathematician" from the above link ...
There are some further reasons why using 0^0 = 1 is preferable, but they boil down to that choice being more useful than the alternative choices, leading to simpler theorems, or feeling more “natural” to mathematicians. The choice is not “right”, it is merely nice.