# The Power of Zero, the third index law. In general: This formula tells us that any number, except 0, raised to the power zero has a numerical value of 1.

If x = 1 any power = 1 so x to the zero power = 1. If x is not equal to 1 any power is not equal to one except the power of zero 2^x doubles so 2 to the power of zero is half of two = 1 5^x is 5, 25 125 so increases five fold so 5to the power of 0 is 5/5 = 1

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Answer This list of numbers 2 0 = Any number (except 0) raised to the zero power is always equal to 1. 1. 2 1 = Any number Write 2x–1 using only positive exponents. The negative power will become just "1 " once I move the base to the other side of the fraction line. Anything Covers the basic exponent rules, explaining how to remember them and use them properly, especially to simplify Anything to the power 1 is just itself, since it's "multiplying one copy" of itself. So the Simplify [(3x A number other than 0 taken to the power 0 is defined to be 1, which follows from the It can also be seen more intuitively by noting that repeatedly taking the or, ab-b = a0.

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Therefore, you can also write the problem as 1 0. To find the answer, you may think that the answer is 1 times itself 0 times, which is 0. However, that is not the correct answer because of the following rule: Zero to the power of zero, denoted by 00, is a mathematical expression with no agreed-upon value. The most common possibilities are 1 or leaving the expression undefined, with justifications existing for each, depending on context.

### It means if the power of a base is zero then the value of the solution will be 1. Example: Simplify 5 0. In this question, the power of base is zero, then according to the zero property of exponents, the answer of this non zero base is 1. Hence, 5 0 = 1. Negative Property of exponent:

However, your teacher probably didn’t explain why, and knowing the “Why?” is key to genuinely understanding this rule about exponents. Patreon: https://www.patreon.com/H3VtuxMy attempt at making an instructional visual explanation. Music is by Eric Prydz. Discover a pattern that explains why any non-zero number to the zero power equals one.

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But we could also think of 00 having the value 0, because zero to any power (other than the zero power) is zero. In short, the multiplicative identity is the number 1, because for any other number x, 1*x = x.

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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. The other way to picture the calculation of an exponent is to start from the number one and then multiply as the exponent says to.