We know that x^0 = 1
So, the zeroeth root of 1 is x.
If we solve it mathematically, then the value of x is 1.
This contradicts our previous knowledge that x belongs to a set of real numbers.
So, how do we prove that x^0 = 1, where x is any real no., like this? 

Asked by bjayanta | 8th Jun, 2015, 03:03: PM

Expert Answer:

T h e r e space a r e space c e r t a i n space c o n d i t i o n s space o n space u sin g space t h e space l a w s space o f space e x p o n e n t s comma x to the power of 0 equals 1 I f space t h e r e space i s space a n space e q u a t i o n comma x equals a A l s o space w e space h a v e space t o space t a k e space t h a t space x space i s space a n y space r e a l space n u m b e r space b u t space not equal to 0 space o r space 1 rightwards double arrow x to the power of 1 over n end exponent equals a to the power of 1 over n end exponent left square bracket T a k i n g space s q u a r e space r o o t space o n space b o t h space s i d e s comma space p r o v i d e d space n not equal to 0 right square bracket I t space m e a n s space t h e space s q u a r e space r o o t space c a n space o n l y space b e space t a k e n space w h e n space n not equal to 0. F o r space e g colon 1 squared equals 1 cubed i t space d o e s space n o t space m e a n space t h a t space 2 equals 3. T h e space p r o p e r t y space c a n space b e space a p p l i e d space w h e n a to the power of m equals a to the power of n rightwards double arrow m equals n comma space w h e n space a not equal to 0 space o r space 1.

Answered by Prasenjit Paul | 9th Jun, 2015, 09:42: AM