Why division to zero is not allowed or undefined? why any number raised to zero is equal to one?

Answer 1

To the first part - to prove your division - you multiply back out.
6 divided by 3 = 2 2 x 3 = 6

but 0 times ANYTHING is always 0
and you cannot say 0 div by 0 = 439 although 439 x 0 = 0

the second part has me stumped - been out too long!

Answer 2

Take this for example:

0 X a = 0
0 X b = 0

where a and b are real integers.

So if we were to do division then:

a = 0/0
b = 0/0

But a is not equal to b. To put it simply, division by zero is undefined since there is no definite answer to it.

We could also look at it this way. We assmue that a number is divisible by zero say 3/0 = C If we multiply C by zero we would not get 3, since C x 0 = 0.

As for the question, we need to look at the law of indices. The law of indices state that:

a^m / a^n = a^(m-n)

3^0 = 3^(5-5) = 3^5 / 3^5 = 1

Hope this helps!

Answer 3

simply....it is a matter of logic

we have a rule in math: Limitaion (any number/infinity) gives us zero

so,if u have an infinity , and divided it by any number it shoul gives u infinity.... 1,2,3, ....1000000, ... all these numbers can be considered infinity to small numbers like .32323*10^-431434 .....right? So, there is no definition of infinity here..... and so it is undefined

raising to zero: if u raise any number to a fraction.. i.e: .5, .25 or such things... u find the roots of that number.
if the fraction is to small...1/1000 .. that means there is a number to be powred 1000 times to give you the specified number. tat means the roots is (1+fraction)..this fraction will be smaller and smaller until it is zero.

Answer 4

Well you cant divide by zero because it would defy the conventions of mathematics.

z^0 = z^1/z^1 i.e z^(1-1)
if z^1 = x

x/x =1