Exponents i think..

HELLO !!  math people ^.^
I'm a bit late..well i'm really late because of some technical difficulties:(.

so lets get started with a math-christmas photo since its CHRISTMAS!!
and like a total nerd im doing a blog xP
oh well,  here the picture:

       
I dont know if HO3, is a chemistry component or a math picture but what ever I think the bear is super dupper cute 
>.<.

now that the picture is over, we are going to solve the question of the day :

How do we simply expressions with rational exponents?

so lets start with a simple, and easy expression like:

x4

                                                                                                          x-6
because we cannot have a negative exponent in the bottom of the bar we have to switch the negative exponent along with the x and flip it to the opposite side. 

For example: 

given expression : 

x4

                                             x-6
change the negative exponent to the opposite side of the bar. Therefore: 

x4 x6

                                              1
from there,we can say we are multiplying both x's. when we multiply, the exponents are added therefore :

x4x6 :  4+6 

x10

lets try more problems:
x3x(2/4)x-3  = 
Step one : add all exponents 
3+(2/4)+(-3)
3+(-3) =0
0+(2/4) = (2/4)

Step two : combine the answers 
 X(2/4)

Another problem: 
 (X15 Y25 )(1/5)

Step one: first multiply the outside exponent to the inside exponents. 
 (X15 Y25 )(1/5) :
(15)(1/5)
multiply straight across so it would be :
X:   15 x 1  = 15 = 3  
       1      5      5

Y:   25 x 1 =  25 = 5
       1      5      5

Step Two:  combine the exponents to its appropriate variable.
X3Y5


NOW YOU TRY :D

X-3
X2

X (-9/18)
X3

Works cited :
picture : http://i1.cpcache.com/product/180766012/ho_ho_ho_christmas_math_humor_teddy_bear.jpg?height=150&width=150