how to prove a number to the zero power is one?

Prove that  a ⁰ = 1 ?

(How to prove that a number to the zero power is one)

To solve this problem you need to some basic concept of mathematical algebra. These concepts are  following .

Rule no. 1

First, any number raised to the power of "one" equals itself. These makes sense, because the power shows how many times the base is multiplied by itself. If it's only multiplied one time, then it's logical that it equals itself.

Secondly, one raised to any power is one. This, too, is logical, because one times one, as many times as you multiply it, is always equal to one.

Rule no. 2 (product rule)

The exponent "product rule" tells us that, when multiplying two powers that have the same base, you can add the exponents. In this example, you can see how it works. Adding the exponents is just a short cut!

Rule no. 3(power rule)

The "power rule" tells us that to raise a power to a power, just multiply the exponents. Here you see that 5² raised to the 3rd power is equal to 5⁶.

Rule no. 4 (Quotient Rule)

The quotient rule tells us that we can divide two powers with the same base by subtracting the exponents. You can see why this works if you study the example shown.

And now we are going to prove  that a number to the zero power is one ,lets prove it .

How to prove that a number to the zero power is one:

from the property 4 of algebra which is given Above 

when  we consider m=n;

then,

5³/5³=5⁰;

5⁰=1;

this is the main reason for a number to the zero power is one.

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