Who is asking: Teacher
How do I explain to kids that i.e. 5 exponent 0 = 1?
Does 0 exponent 0 = 1?
By applying the rule for exponents of quotients you can show that
But we know that any rational expression (fraction) that has the same thing in the numerator and the denominator is equal to 1.So
By the transitive property, a0 is therefore equal to 1.
00 is more complicated since you cannot do an analogous demonstration with it because 0 raised to a finite power is 0 and you can therefore not have it in the denominator of a fraction. 00 is undefined.
Our response to another teacher who asked about 00 may help clairfy why 00 should remain undefined.
Hope this helps.
Leeanne and Penny