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First, let’s refer to the combinational definition. 2019-11-04 · You may have learned in school that anything, whether it’s a variable or a constant, to the power of zero is equal to one. However, your teacher probably didn’t explain why, and knowing the “Why?” is key to genuinely understanding this rule about exponents. Watch this short video to understand why! Originally Answered: Why any number to the zero power always gives a one? When x^2 is multiplied with x^3, their powers will get added as simplification of the equation will be (x*x)* (x*x*x)=x*x*x*x*x=x^5.When So, if we do x^2*x^0, their powers get added and we get x^2. Showing that anything raised to the power of 0 equals one is a fairly trivial matter.
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Looking at the pattern established when a number is raised to different powers, each one less than the next, helps explain the concept.
But a^x is equal to a^y, since x = y; hence a^x/a^y = 1. Therefore, by Transitive property of Equality, a^0 = 1. Thus, this result says that number raised to the power zero is equal to 1.
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Hence, 5 0 = 1.
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x to the power of 1 is x. x to the 0 power is defined as x/x=1. x to the power of -1 is 1/x. x to the power of -2 is 1/x / x = 1/(x^2) It's a logical geometric progression on either side, but there's no reason for x to the zero power to make 1.