# Why isn't $$\frac 00$$ simply 0?

A number $$x$$, to the power $$a$$, and another arbitrary constant $$b$$, can be considered as follows: $$\dfrac{x^{a+b}}{x^b}$$. Simplifying this fraction, through rules of exponents, we know that it is the same as $$x^{a+b - (b)} = x^a$$. So let's look at 0. $$0^1 = \dfrac{0^{1+2}}{0^2}$$. Since we know both $$0^1$$ and $$0^2$$ are 0, does it not follow that $$\dfrac00 = 0$$?

Note by M K
1 year, 9 months ago

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The rules of exponents are for non zero $$x$$.

As such, division by zero is undefined.

- 1 year, 9 months ago

Ah I see. Thanks for clarifying!

- 1 year, 9 months ago

You're welcome. :)

- 1 year, 9 months ago

0/0 can't be 0 cos it is undefined or sometimes be intermediate. You can confirm using your calculator. That why calculator can't solve such problem.

- 1 year, 9 months ago