Why is 4 to the power 0 equal to 1?

Answer 1

for any non zero no. x, x^0=1

the proof is as follows, consider the two no.s x^m and x^n,where m and n are two non zero no.s. now let us assume without any oss of generality,that m>n,hence (x^m)/x^n=(x*x*x....m times)/(x*x*x...n times)

now on the r.h.s, n no. of x in the denominator will cancel out n no. of x in the numerator(as x is non zero);leaving (m-n) no. of x in the numerator,

i.e. (x^m)/(x^n)=x^(m-n)

now letting m=n,we have

x^m/x^m=x^(m-m)

or, 1=x^0

hence the proof

if x is also 0,i.e. 0 to the power 0 is undefined!