What does 0 to the power of 0 equal?
one
Any non-zero number to the zero power equals one. Zero to any positive exponent equals zero.
Why can’t you do 0 to the power of 0?
Thus 0 to the power 0 is undefined! 0 to any positive power is 0, so 0 to the power 0 should be 0. But any positive number to the power 0 is 1, so 0 to the power 0 should be 1. We can’t have it both ways. Underlying this argument is the same idea as was used in the attempt to define 0 divided by 0.
What is 0 raised to any power?
On one hand, any other number to the power of 0 is 1 (that’s the Zero Exponent Property ). On the other hand, 0 to the power of anything else is 0 , because no matter how many times you multiply nothing by nothing, you still have nothing.
What does an exponent of 0 mean?
1
The rule for zero as an exponent: Any nonzero real number raised to the power of zero is one, this means anything that looks like a 0 a^0 a0 will always equal 1 if a is not equal to zero.
What is a number that is raised to the power 0?
0.1 raised to the power 0 is 1. 0.01 raised to the power 0 is 1. 0.001 raised to the power 0 is 1. Continuing that you’ll come to numbers that small, that you’ll have hard time distinguishing them form 0, and still the result will be 1. If almost-pratcically-nothin-at-all raised to the power 0 is 1, then why not nothing?
What is 0/0 to the zero power?
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?
What does it mean to raise to the power of 1?
Raise a number to the power of 1 means you have one of that number, raise to the power of 2 means you have two of the number multiplied together, power 3 means three of the number multiplied
Why is 0\%0 defined as equaling 1?
0 0 is one such exception to this. It is defined as equaling 1 because there are many examples of math that require it to be 1, and no counterexamples where defining it as 1 causes problems. My go-to example for why it needs to be defined as 1 is the binomial expansion: ( a + b) n = ( n 0) a n b 0 + ( n 1) a n − 1 b 1 + ( n 2) a n − 2 b 2 + …