×

# 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 ago

Sort by:

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

As such, division by zero is undefined. · 1 year ago

Ah I see. Thanks for clarifying! · 1 year ago

@M K You're welcome. :) · 1 year ago