SOLUTION: Simplify each expression. Use only positive exponents. (2r^-1 s^2 t^0)^-2 /2rs Note: I left a space in the parenthesses so that you would know that 2r^-1, s^2 and t^0 are in t

Algebra ->  Exponents -> SOLUTION: Simplify each expression. Use only positive exponents. (2r^-1 s^2 t^0)^-2 /2rs Note: I left a space in the parenthesses so that you would know that 2r^-1, s^2 and t^0 are in t      Log On


   



Question 64756This question is from textbook
: Simplify each expression. Use only positive exponents.
(2r^-1 s^2 t^0)^-2 /2rs
Note: I left a space in the parenthesses so that you would know that 2r^-1, s^2 and t^0 are in the parenthesses.
This question is from textbook

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!

Simplify each expression. Use only positive exponents.
(2r^-1 s^2 t^0)^-2 /2rs 
Note: I left a space in the parenthesses so that you 
would know that 2r^-1, s^2 and t^0 are in the 
parenthesses.

+%282r%5E-1s%5E2t%5E0%29%2F%282rs%29+

Give every factor an exponent of 1 if none shows

+%282%5E1r%5E-1s%5E2t%5E0%29%2F%282%5E1r%5E1s%5E1%29+

We divide top and bottom by 2%5E1

+%28r%5E-1s%5E2t%5E0%29%2F%28r%5E1s%5E1%29+

We know that t%5E0 equals 1, so

+%28r%5E-1s%5E2%2A1%29%2F%28r%5E1s%5E1%29+

We can dispense with the 1

+%28r%5E-1s%5E2%29%2F%28r%5E1s%5E1%29+

Now we use the rule for getting rid of negative
exponents.  The rules are:

1. If a factor of the numerator has a negative
   exponent, then eliminate base and exponent
   from the numerator, and place a factor which
   has the same base but the opposite signed,
   i.e., positive exponent, as a factor of the
   denominator.

2. If a factor of the denominator has a negative
   exponent, then eliminate base and exponent
   from the denominator, and place a factor which
   has the same base but the opposite signed,
   i.e., positive exponent, as a factor of the 
   numerator. 

We need the first rule to eliminate the r%5E-1
from the numerator and place r%5E%281%29 in the
denominator. 

+%28s%5E2%29%2F%28r%5E1r%5E1s%5E1%29+

Next we add the exponents of r in the denominator, i.e.
r%5E1r%5E1 = r%5E%281%2B1%29 = r%5E2


+%28s%5E2%29%2F%28r%5E2s%5E1%29+

Finally subtract the exponents of s, 2-1 = 1,

+%28s%5E1%29%2F%28r%5E2%29+

or just

s%2Fr%5E2

Edwin