Zero and Negative Exponents.

[cheri_125]

Hey,
I have a question about negative exponents.

-1/2-1.

How would I find the answer for it.
Step by step, please. Im kind of slow at math >.<

Thankss!!!

--Cheri_125 <3

Comments

[notmrgarrison]

I'm guessing that's (-1/2)-1

In general, x-1 = 1/x, so (-1/2)-1 = 1/(-1/2) = -2.

More generally x-a = 1/xa

[cheri_125]

Thanks :)

[the_whybird]

To help understand why this might be, consider that we probably want zero and negative exponents to keep as many of the properties of positive ones as we can.

One of the things about positive exponents is that if you have two numbers multiplied together (like (2324) then you add the exponents (to get 2(3+4)), because you're just multiplying the same number together a whole load of extra times.

If we want to keep this rule for negative exponents, then we know already that we want 22 * 2-1 to be 22-1 = 21 = 2. So the only number that 2-1 can possibly be is 1/2.

You can work with a similar sort of chain of thought to figure out what 20 ought to be, or even fractional powers like 21/2

One final note: Because two numbers multiplied together always give you a positive, when you're squaring a negative number you always have to be careful about where the brackets go, because (-1)2 is (-1) * (-1) which is 1, but -(12) is -( 1 * 1 ) which is -1. So it makes a big difference where the brackets are!

[cheri_125]

Thank you!