SOLUTION: 3 to the -x power is equal to (1/3) to the x power....how do i prove this mathematically?

Algebra ->  Trigonometry-basics -> SOLUTION: 3 to the -x power is equal to (1/3) to the x power....how do i prove this mathematically?      Log On


   

Question 133378: 3 to the -x power is equal to (1/3) to the x power....how do i prove this mathematically?
Found 2 solutions by jim_thompson5910, vleith:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
3%5E%28-x%29 Start with the given expression



1%2F3%5Ex Since we have a negative exponent, this means that we flip the base 3 to get 1%2F3%5Ex


1%5Ex%2F3%5Ex Rewrite 1 as 1%5Ex


%281%2F3%29%5Ex Factor out the exponent


So this shows us that 3%5E%28-x%29=%281%2F3%29%5Ex

Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
+3%5E%28-x%29+=+1%2F3%5Ex++
This is not %281%2F3%29x
To prove +3%5E%28-x%29+=+1%2F3%5Ex++
Given +3%5E%28-x%29+
+3%5E%28-x%29+=+3%5E%28-x%29+%2A+1++
+3%5E%28-x%29+=+3%5E%28-x%29+%2A+%283%5E%28x%29%2F3%5E%28x%29%29++
+3%5E%28-x%29+=+%283%5E%28-x%29+%2A+%283%5E%28x%29%29%2F%283%5E%28x%29%29%29++
+3%5E%28-x%29+=+%28%283%5E0%29%2F%283%5E%28x%29%29%29++
+3%5E%28-x%29+=+1%2F%283%5E%28x%29%29++