8 to power 0=1 prove it
Answers
Answered by
0
obviously it is one because any numbers power zero is one
Answered by
0
What About Zero to the Zero Power?
This is where things get tricky. The above method breaks because, of course, dividing by zero is a no-no. Let’s examine why.
We’ll begin with looking at a commondivide by zero ERROR.
How about 2÷0? Let’s look at why wecan’t do this.

Division is really just a form of multiplication, so what happens if I rewrite the above equation as:

What value could possible satisfy this equation for x?
There is no value! Any number times zero results in zero, it can never equal 2. Therefore, we say division by zero is undefined. There is no possible solution.
Now let’s look at 0÷0.

Again, rewrite it as a multiplication problem.

Here we encounter a very different situation. The solution for x could be ANY real number! There is no way to determine what x is. Hence, 0/0 is considered indeterminate*, not undefined.
If we try to use the above method with zero as the base to determine what zero to the zero power would be, we come to halt immediately and cannot continue because we know that 0÷0 ≠ 1, but is indeterminate.
So what does zero to the zero power equal?
This is highly debated. Some believe it should be defined as 1 while others think it is 0, and some believe it is undefined. There are good mathematical arguments for each, and perhaps it is most correctly considered indeterminate.
Despite this, the mathematical community is in favor of defining zero to the zero power as 1, at least for most purposes.
Perhaps a helpful definition of exponents for the amateur mathematician is as follows:
This is where things get tricky. The above method breaks because, of course, dividing by zero is a no-no. Let’s examine why.
We’ll begin with looking at a commondivide by zero ERROR.
How about 2÷0? Let’s look at why wecan’t do this.

Division is really just a form of multiplication, so what happens if I rewrite the above equation as:

What value could possible satisfy this equation for x?
There is no value! Any number times zero results in zero, it can never equal 2. Therefore, we say division by zero is undefined. There is no possible solution.
Now let’s look at 0÷0.

Again, rewrite it as a multiplication problem.

Here we encounter a very different situation. The solution for x could be ANY real number! There is no way to determine what x is. Hence, 0/0 is considered indeterminate*, not undefined.
If we try to use the above method with zero as the base to determine what zero to the zero power would be, we come to halt immediately and cannot continue because we know that 0÷0 ≠ 1, but is indeterminate.
So what does zero to the zero power equal?
This is highly debated. Some believe it should be defined as 1 while others think it is 0, and some believe it is undefined. There are good mathematical arguments for each, and perhaps it is most correctly considered indeterminate.
Despite this, the mathematical community is in favor of defining zero to the zero power as 1, at least for most purposes.
Perhaps a helpful definition of exponents for the amateur mathematician is as follows:
Similar questions