# negative exponents

• Mar 31st 2008, 04:23 PM
Jerry Cunningham
negative exponents
I am lost on this problem.
-2^-3
-1/2^3
I think I understand up to here. But where does the double negative come in on this next step?
--1/2*2*2
--1/4*2
--1/8
-*8/8-1/8
-8/8-1/8
-8-1/8
-9/8
• Mar 31st 2008, 05:42 PM
TheEmptySet
Quote:

Originally Posted by Jerry Cunningham
I am lost on this problem.
-2^-3
-1/2^3
I think I understand up to here. But where does the double negative come in on this next step?
--1/2*2*2
--1/4*2
--1/8
-*8/8-1/8
-8/8-1/8
-8-1/8
-9/8

$\displaystyle -2^{-3}$

The exponent only applies to the base in this case the 2 NOT the negative sign.

If you like you can think of it this way.

$\displaystyle (-1)2^{-3}=\underbrace{\frac{-1}{2^3}}_{\mbox{Law of neg exp.}}=\frac{-1}{8}$
• Mar 31st 2008, 10:56 PM
earboth
Quote:

Originally Posted by Jerry Cunningham
...But where does the double negative come in on this next step?
-1-1/2*2*2
-1-1/4*2
-1-1/8
-*8/8-1/8
-8/8-1/8
-8-1/8
-9/8

I assume that there is a typo.
• Apr 2nd 2008, 04:52 AM
ice_syncer
Quote:

Originally Posted by Jerry Cunningham
I am lost on this problem.
-2^-3
-1/2^3
I think I understand up to here. But where does the double negative come in on this next step?
--1/2*2*2
--1/4*2
--1/8
-*8/8-1/8
-8/8-1/8
-8-1/8
-9/8

That's very wrong

according to the question we need to find what -2^-3 is,

now get rid of the negative integer by converting the base(-2) to a fraction

so this implies (1/-2)^3

now it's easy, the answer is 1/-8

but we need to convert this to standard from, so we multiply both sides of the fraction by -1

so the final answer is -1/8

next time, try separating the exponents from the base with a parenthesis

(Emo)