Question

Prove that x ^ 0 = 1​

Answer 1

Answer:

To prove:

X^0=1

Any by power 0 is one

Proof :

1*x*x*x=x^3

1*x*x=x^2

1*x=x^1

1=x^0

Hence proved..

Answer 2

We know that any number raised to the power 0 is 1. But how do we prove it?

A simple proof is given below. Here we may use a concept,

$x^{m-n}\ =\ \dfrac{x^m}{x^n}$

So,

$x^0=x^{1-1}=\dfrac{x^1}{x^1}=1$

Done!

Instead of 1, we can use any other number.

$\bullet\ x^0=x^{2-2}=\dfrac{x^2}{x^2}=1\\ \\ \\ \bullet\ x^0=x^{-3+3}=x^{(-3)-(-3)}=\dfrac{x^{-3}}{x^{-3}}=1\\ \\ \\ \bullet\ x^0=x^{\frac{1}{2}-\frac{1}{2}}=\dfrac{x^{\frac{1}{2}}}{x^{\frac{1}{2}}}=1\\ \\ \\ \bullet\ x^0=x^{a-a}=\dfrac{x^a}{x^a}=1$

According to  $x^{m+n}=x^m\times x^n,$  we also write,

$x^0=x^{-3+3}=x^{-3}\times x^3=\dfrac{1}{x^3}\times x^3=\dfrac{x^3}{x^3}=1$

Hence Proved!