What will be the result when zero is raised to a power of zero?
by definition, zero to the zero power is one. That allows the function a^a to be continous at a=0
There's a nice discussion of this topic at
http://mathforum.org/dr.math/faq/faq.0.to.0.power.html
Sorry -- it's turtles all the way down.
When zero is raised to the power of zero, the result is undefined and it leads to an indeterminate form. This means that there is no universally agreed-upon answer for this particular calculation.
To understand why it is undefined, let's break it down:
Any number (except zero) raised to the power of zero is defined to be equal to 1. This is a convention in mathematics. For example, 2^0 = 1, 3^0 = 1, etc.
However, when we consider zero raised to the power of zero, there are conflicting mathematical arguments:
Argument 1: Zero raised to any positive power is always zero. So, by extension, zero raised to the power of zero should also be zero.
Argument 2: Any number (except zero) raised to the power of zero is defined to be equal to 1. So, following this convention, zero raised to the power of zero should be 1.
These conflicting arguments have led to debates in mathematics, and there is no consensus on the value of zero raised to the power of zero. Different fields of mathematics, such as calculus, number theory, and combinatorics, may define the value differently based on their specific needs and contexts.
Therefore, it is important to note that the result of zero raised to the power of zero is considered to be undefined, and there is no definitive answer.