Infinity.
It remains as zero
Infinity.
Two raised to the seventh power is 128.
0.02 raised to the fourth power is 0.00000016
Any number raised to the power of 0 is always 1
(-infinity, infinity)
It would be infinity raised to the infinite power and that value raised to the infinite power. netflyer
It remains as zero
The value of anything raised to the power of infinity depends on the base. If the base is greater than 1, the value approaches infinity. If the base is equal to 1, the value remains 1. If the base is between 0 and 1, the value approaches 0. If the base is 0, the expression is typically considered to be 0, but if it's 0 raised to the power of infinity, it is an indeterminate form.
The answer is not 1. While it may seem like 1 raised to anything equals 1 (because 1x1=1, and 1x1x1=1, ad infinitum), this is actually not the case. The answer is that 1 raised to infinity is indeterminate. When dealing with infinity, you are talking about a non-finite number, so that essentially throws all rules about algebra out the window.
0 raised to any number is 0
Infinity raised to the power of zero (∞^0) is an indeterminate form in mathematics. This means that it does not have a definitive value and can lead to different results depending on the context in which it appears. In some cases, it can be interpreted as 1, while in others, it may lead to different conclusions based on limits and the specific functions involved. Thus, careful analysis is required to evaluate expressions involving infinity raised to the power of zero.
E to the power infinity, or lim en as n approaches infinity is infinity.
It's indeterminate.
If you raise 2 to an infinite power, you get a higher-order infinity. It is still infinity, but a larger number. For example, 2 to the power beth-0 is equal to beth-1; 2 to the power beth-1 is equal to beth-2, etc. Beth-0 is the infinity of counting numbers and integers, beth-1 is the infinity of real numbers, and with beth-2, it gets a bit hard to visualize. Among other things, beth-2 is the infinity of all possible functions over real numbers.
Infinity.
This integral cannot be performed analytically. Ony when the integral is taken from 0 to infinity can it be computed by squaring the integral and applying a change of variable (switching to polar coordinates). if desired I could show how to do this.