Expert: Paul Klarreich - 4/11/2006

Question
Simplify:

2^-1/(2^-2 +2^-3)  It says hint: multiply numerator and denominator by 2^3  So, it is 2 to the negative 1 divided by 2 to the negative 2 + 2 to the negative 3.  I appreciate your help.  Thank you once again.

Answer
Hi, Colleen,

Subject:  Trig - simplifying exponents
Question:  Simplify:

2^-1/(2^-2 +2^-3) It says hint: multiply numerator and denominator by 2^3 So, it is 2 to the negative 1 divided by 2 to the negative 2 + 2 to the negative 3. I appreciate your help. Thank you once again
--------------------

You have something called a complex fraction (a fraction whose numerator and/or denominator contain fractions):
   1  
  ---
  2^1
----------
1     1
--- + ---
2^2   2^3

You simplify by multiplying every term by the LCD of all the fractions, in this case  2^3.  Then you get an ordinary fraction:

 2^2
-------
2^1 + 1

   4
= -----
 2 + 1

= 4/3