why this is true? a^0=1 (0 ≠ a)?

My friend, notice that a^-k=1/(a^k)

thus a^(0)=a^(k-k)=(a^k)(a^-k)=(a^k)(1/(a^k))=1

thus a^0=1, to answer why 0 is not equal to a is clearly harder because even mathematician cannot solve them yet.

This is the definition of (anything) raised to the power of zero.

Think of it this way:

a^1 = 1* (a)

a^2 = 1*(a * a)

a^3 = 1*(a * a * a)

so a^0 = 1* _______ (blank, nothing! no a's to multiply so keep it at 1)

It's just not there.

This explaination is not legit, but its how I explain to students when I teach.

0^0 is not defined. Think about: How can you have 0 no times?

0^1 = 0

0^2 = 0*0

0^3 = 0*0*0

Just like the examp[le with the a, this is just my reasoning to make learning easier. 0^0 is just...NOT THERE!

because 0^0 is undefined; therefore, a certainly cannot equal 0 in this equation.

ANYTHING to the power of zero is 1, EXCEPT 0 itself.

ex.

1^0 = 1

5^0 = 1

193848234^0 = 1

hahaha is your teacher trying to get you to answer this because it is like a mystery of mathematics that is just accepted at true.