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 $\dfrac00 = 0$ ?

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Comments

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

As such, division by zero is undefined.

A Former Brilliant Member - 4 years, 10 months ago

Ah I see. Thanks for clarifying!

M K - 4 years, 10 months ago

You're welcome. :)

A Former Brilliant Member - 4 years, 10 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.

Ayanlaja Adebola - 4 years, 10 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Why isn't 00 \frac 00 00​ simply 0?

Comments

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