Question

Prove a0 = 1.
With full explanation. I need it urgently.
Who will explain with full explanation I will follow them and I will thank their all answers. ​

Answer 1

Step-by-step explanation:

Simple “Proof” Why Zero Factorial is Equal to One

What it means is that you first start writing the whole number n then count down until you reach the whole number 1. For the equation to be true, we must force the value of zero factorial to equal 1, and no other. Otherwise, 1! ≠1 which is a contradiction.

Answer 2

Given:

a is a numeric

To find:

Prove a⁰ = 1.

Solution:

Let's prove this in steps.

An exponent is expressed in the form 'a' raised to the power 'b'

aᵇ

When the exponent ab is divided by itself, we get the expression:

a/a = 1

aᵇ/aᵇ = 1

aᵇ⁻ᵇ = 1

a⁰

Since we know a number divided by itself always results in 1,

aᵇ/aᵇ =1 (I)

Also,  

aᵇ÷aᵇ

= aᵇ/aᵇ

(Using the quotient law of exponents)

aᵇ⁻ᵇ = a0 . (II)

From (I) and (II)

a0 = 1

OR

We can start with the equation

1 = 1

We also know that a number divided by itself is 1.

a/a = 1

a²/a² = 1

a²⁻² = 1

a⁰