Some people claim that 00=1 0 ^ 0 = 1 00=1. = Example 9.   Argument 2: With respect to limits, if lim⁡x→af(x)=lim⁡x→ag(x)=0\lim_{x \to a} f(x) = \lim_{x \to a} g(x) = 0limx→a​f(x)=limx→a​g(x)=0, then lim⁡x→af(x)g(x)\lim_{x \to a} f(x)^{g(x)}limx→a​f(x)g(x) doesn't necessarily tend to any particular value. is 0 2 Already have an account? Consider a to the power b and ask what happens as a and b both approach 0. 0 0 Zero to the Power of Zero What is 0 0 ?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. = of Powers Property, CCNA Collaboration - Cisco Certified Network Associate-Collaboration Courses & Classes, CCNA Service Provider - Cisco Certified Network Associate-Service Provider Courses & Classes, CTP - Certified Treasury Professional Test Prep, CRISC - Certified in Risk and Information Systems Control Test Prep, MCSE - Microsoft Certified Solutions Expert Courses & Classes, CIA - Certified Internal Auditor Test Prep.   We must define x^0=1 for all x , if the binomial theorem is to be valid when x=0 , y=0 , and/or x=-y . Answer: Zero to zeroth power is often said to be "an indeterminate form", because it could have several different values. , or Learn more in our Algebra Fundamentals course, built by experts for you. 0 0 By contrast, the function 0^x is quite unimportant. So this says, 0 a The U.S. National Debt is setting the stage for massive tax increases within the next 10 years and will impact a retiring generation of Baby Boomers. This is also the same reason why anything else raised to the power of 0 is 1. lim⁡x→0+x1ln⁡x? However, in the case of -1 0, the negative sign does not signify the number negative one, but instead signifies the opposite number of what follows. As of 4/27/18. But 0 to the -5th power is 1 over 0 which is undefined and same with 0 to the -100th power. Award-Winning claim based on CBS Local and Houston Press awards. Varsity Tutors © 2007 - 2020 All Rights Reserved, Product 0   It looks like 0⁰ = 0. Power of Zero In general: This formula tells us that any number, except 0, raised to the power zero has a numerical value of 1. Some textbooks leave the quantity 0^0 undefined, because the functions 0^x and x^0 have different limiting values when x decreases to 0. Certainly, 0−10^{-1}0−1 does not equal 0, since we cannot divide by 0. But 0 to the -5th power is 1 over 0 which is undefined and same with 0 to the -100th power.   Supercharge your algebraic intuition and problem solving skills! In order for this to hold for x=0x = 0x=0 and n=1 n = 1n=1, we need 00=10^0 = 100=1. Reply: Mathematics is a subject built upon definitions--there is no "universal truth" of what 000^000 really equals. 0 *See complete details for Better Score Guarantee. Varsity Tutors does not have affiliation with universities mentioned on its website. If it is convenient for the binomial theorem to assume 00=1,0^0=1,00=1, that is fine. This contradiction means 000^000 should be left undefined. . 2, We know that   Underlying this argument is the same idea as was used in the attempt to define 0 divided by 0. Zero ( Do It Faster, Learn It Better. Instructors are independent contractors who tailor their services to each client, using their own style, still be true! 0 =