Final answer:
The value of e to the power of negative infinity is zero. This is understood by considering the reciprocal property of exponents: as the negative exponent approaches negative infinity, the overall value approaches zero.
Step-by-step explanation:
The student has asked 'What is e to the power of negative infinity?'. In mathematics, when considering limits, if we take e (where e is the base of the natural logarithm, approximately equal to 2.71828) to the power of negative infinity, we calculate a limit. As the exponent goes to negative infinity, the value of e to that power approaches zero. This is because e-∞ is essentially like having 1 divided by e raised to the power of positive infinity, which is an infinitely large number. Therefore, the result is an infinitely small number, which is conceptually zero.
To understand this better, consider the laws of exponents where a negative exponent implies taking the reciprocal. For example, x-n = 1/xn. As n increases infinitely, the value of xn becomes infinitely large, making 1/xn infinitely small. Applying this to e, e-∞ is the same as 1/e∞, which tends to 0 as e∞ tends to infinity.