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Q: What does the Number e to the power of zero equal?

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Not necessarily. i times pi is not a whole number, and yet e to the power of i times pi is equal to -1.

Here is why any number to the zero power equals one. Consider this. a^b. it is natural to restrict a > 0, but we'll only assume that number b is any real number. We'll use the natural exponential function defined by the derivative of the exponential function. Now we have a^r=e^rln(a). And we know that e^rln(a)=e^((ln(a))^r), where a >0 and r is in the domain of all real numbers negative infinity to infinity. We can apply this definition to any number a to any power r. Particularly, a^0. By the provided definition, a^0=e^(0*ln(a))=e^0=1. Furthermore, a^1=e^(1*ln(a))=e(ln(a))=a. And a^2=(e^(ln(a))^2)=a^2.

Zero.

A positive number, raised to any power, is positive.

in energy signal power iz zero according to this equation P=E/2T

e is not an imaginary number. e is Euler's constant.Uh...imaginary numbers can equal almost any number in math; it depends upon the application.Imaginary numbers can represent 1 or -1; it depends upon the applicaiton.1e is not prime; it is Euler's constantNothing in the question I posted has an exponent of zero. (You may want to ask a math professor to explain why a number with an exponent of zero is equal to one.)You may want to ask a math professor to explain what an imaginary number means in math.You may want to ask a math professor or someone else to explain what the smalest value is that solves tan ex = 1.e=mc2 is a totally different problem, a totally different value for e. In that case e = energy, m = mass and c = the speed of light. Different application.The number e to the power of zero is not an issue in this problem (it equals 1)An exponent can be a positive or negative number.

that would be the inverse of e to the plus infinity Answer is thus zero

Zero

no number can be raised to a power and equal 0 (x^y can never = 0). e is positive (about 2.7) and any positive number can not be raised to a power and equal negative (positive number X positive number = positive number)

It is possible.

The answer is "no solution." ln(0) means e^x=0, and nothing raised to any power can ever equal zero. The domain of y=lnx is (0,∞) and the range is (-∞,∞).

This follows immediately from the first Sylow theorem.

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