Question

prove that x power 0 is equal to the 1

Answer 1

xⁿ means x multiplied by itself n times

So, x^0 means x multiplied by itself 0 times which gives 0

Answer 2

process 1

To Prove:- x^0=1

We know that x^0=x×x (0 Times)

we all know 1−1=0

so we can say that x^0=x^[1−1]

Now We Got x^0=(x^1)×(x^−1)

x^0=x^1×[1/x^1]

where x^1 and x^1 gets cancelled

Now we got x^0=1  Hence Proved

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process 2

Let's look at what it means to raise a number to a certain power: it means to multiply that number by itself a certain number of times. Three to the second power is three multiplied by itself 2 times, or 3*3=9. Let's look at a few examples:

3^5 = 3*3*3*3*3 = 243

3^4 = 3*3*3*3 = 81

3^3 = 3*3*3 = 27

3^2 = 3*3 = 9

3^1 = 3 = 3

But how do you go from 31 to 30? If you look at the pattern, you can see that each time we reduce the power by 1 we divide the value by 3. Using this pattern we can not only find the value of 30, we can find the value of 3 raised to a negative power! Here are some examples:

3^0 = 3/3 = 1

3^-1 = 1/3 = 0.3333... (this decimal repeats forever)

No matter what number we use when it is raised to the zero power it will always be 1

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