maths problem: please help me?

Question

why a^0=1
why every no. having power zero is 1.

Answer 1

Wikipedia page explans it pretty well

The meaning of 35 may also be viewed as 1 × 3 × 3 × 3 × 3 × 3: the starting value 1 (the identity element of multiplication) is multiplied by the base as many times as indicated by the exponent. With this definition in mind, it is easy to see how to generalize exponentiation to exponents one and zero:

Any number to the power 1 is itself.

Any nonzero number to the power 0 is 1.
(The case of 00 is discussed below).

One way to prove it is with an addition problem
x^4/x^2 = x^2 -- you always subtract exponents when dividing

3^3/3^2=3^1
27/9=3
this will work for any number
what if i did 3^3/3^3 === when we subtract exponents we take smaller # and move it top the top and subtract exponent
so 3^3/3^3 = 3^0 === or you can say it equals 1/3^0 since you can choose to move it to the bottom since they are equal big

So the answer is 3^0 or 1/3^0

A simpler way would have been to look at the problem
3^3/3^3 = 1 cause anything divided by itself is 1
if you did the exponents first
27/27 =1

So 3^3/3^3 = 27/27 = 3^0 +1/3^0 = 1
They all equal 1

Answer 2

When any mathematical quantity is raised to a power it means it is multiplied by itself, the no. of times mentioned in the power.
eg. 2^3 = 2*2*2 = 8
this can also be written as
2^3 = (2*2*2)*1 = 8*1 = 8
2^1 = 1*(2) = 2
simmilarly,
2^n = 1*(1*2*2*.......n times)
therefore,
when n=0
2^0 = 1*(1 * 0 times 2) = 1

Answer 3

Any number, when multiplied by 0 (zero) is 0 (zero), so I can't work out how you will get 1 as the answer.

Answer 4

Because the base over base = 1

Answer 5

reason:


base
------ =1
base