SOLUTION: I am trying to re-write the following expression using negative exponents: x^2/y^2 The book gives the answer as: y^-2/x^-2 How did they get this? All of the example pro

Algebra ->  Exponents-negative-and-fractional -> SOLUTION: I am trying to re-write the following expression using negative exponents: x^2/y^2 The book gives the answer as: y^-2/x^-2 How did they get this? All of the example pro      Log On


   



Question 28887: I am trying to re-write the following expression using negative exponents:
x^2/y^2
The book gives the answer as:
y^-2/x^-2
How did they get this? All of the example problems about writing equivalent expressions using negative exponents have been limited to single literals, often with the answer containing a 1 in the numerator.

Found 2 solutions by sdmmadam@yahoo.com, longjonsilver:
Answer by sdmmadam@yahoo.com(530) About Me  (Show Source):
You can put this solution on YOUR website!
I am trying to re-write the following expression using negative exponents:
x^2/y^2
The book gives the answer as:
y^-2/x^-2
How did they get this? All of the example problems about writing equivalent expressions using negative exponents have been limited to single literals, often with the answer containing a 1 in the numerator.
Thr rule is
(a)^m = 1/(a)^(-m)
and (x)^(-n) = 1/(x)^n
Therefore
x^2/y^2 = [(x)^2]X[1/y^2]
=[1/x^-2]X[y^-2] (using the above)
=y^-2/x^-2

Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
a%5E%28-3%29 is the same thing as 1%2Fa%5E3... whichever power you have as a "numerator", either positive or negative, the opposite version lies on the denominator.

so x%5E2 is the same thing as 1%2Fx%5E%28-2%29

and 1%2Fy%5E2 is the same thing as y%5E%28-2%29

hence x%5E2%2Fy%5E2 is y%5E%28-2%29%2Fx%5E%28-2%29

jon.