SOLUTION: Very basic question here: Why is any number taken to the 0 power always equaled to 1? (I can't seem to find that answer anywhere.) Thank you.

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Very basic question here: Why is any number taken to the 0 power always equaled to 1? (I can't seem to find that answer anywhere.) Thank you.      Log On


   

Question 952381: Very basic question here: Why is any number taken to the 0 power always equaled to 1? (I can't seem to find that answer anywhere.)
Thank you.
Found 2 solutions by macston, josgarithmetic:
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
Consider what happens as exponents decrease:
x%5E3=x%5E4%2Fx,x%5E2=x%5E3%2Fx, x%5E1=x%5E2%2Fx, so x%5E0=x%5E1%2Fx=1
It is consistent with our description of exponential systems.
According to the law of exponents:
x%5Ea%2Fx%5Eb=x%5E%28a-b%29 so x%5E2%2Fx%5E2=x%5E%282-2%29=x%5E0=1
While not exactly intuitive, we can see that it is consistent within the system.

Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
b%5E4=b%5E4
'
b%5E4%2Fb=%28b%2Fb%29b%5E3=b%5E3
'
b%5E4%2F%28b%5E2%29=%28b%5E2%2Fb%5E2%29b%5E2=b%5E2
'
b%5E4%2Fb%5E3=%28b%5E3%2Fb%5E3%29b=b%5E1=b
'
b%5E4%2Fb%5E4=1

We also have a rule about integer valued exponents:
b%5Ex%2Fb%5Ey=b%5E%28x-y%29 which you will be able to compare with the successive examples just shown.

Briefly, look at b%5E4%2Fb%5E4=b%5E%284-4%29=b%5E0=1, because b%5E4%2Fb%5E4=1.