Can zero to power zero be defined?

[AntonioLao]

One of the properties of exponents as stated in some textbooks for college algebra is that

If a base number [math]b[/math] is raised to power zero the answer is unity if and only if the base is not identically zero.

[math] b^0=1, b \neq 0 [/math]

but if the base represents the quantity of mass, say, mass of an electron, a photon, a gluon, or a graviton, and we are then required to raise this mass to the power zero, if this is done, the result is that, when accepting the logical validity of mathematical truth, only the mass of the electron is defined.

If a TOE is required to raise the mass to power zero then the mass of a majority of elementary particles becomes undefined.

Final question: need we define zero to the power zero?

Final answer: yes. Zero to the power zero is needed to solve the logical entanglement in completing the conceptual development of physical dimension.

[Guille]

I don't know why 0^0 and infinity^0 are taken as indeterminates.

My "proof":

Any number to the power of 0 is/should be itself. That is why we don't right it, when we right 4, we dont right 4^0 because 0 can, in this, be taken away. So, I think 0^0 should = 0. As well as infinity^0 should = infinity.

[AntonioLao]

another property of exponent is that

[math] \frac{a^n}{a^n} = a^{n-n}=a^0=1, a \neq 0 [/math]

for a=0 implies division by zero.

[Guille]

for a=0 implies division by zero.

Then, the so-common "proof" (said to be fallacy) that 1=2, is actually completely true. right?

[AntonioLao]

division by zero is not defined in mathematics.