Why is a number raised to a negative power the reciprocal of that number?
1 Answer
Simple answer:
We'll do this by working backwards.
How can you make
Well, you divide by 2:
How can you make
Well, you divide by 2:
How can you make
Well, you divide by 2:
How can you make
Well, you divide by 2:
Proof why this should be the case
The definition of the reciprocal is: "a number's reciprocal multiplied by that number should give you 1".
Let
Or you can also say the following:
Since both of these are equal to
Divide both sides by
And you have your proof.