SOLUTION: (3^(-1)X^(3)Y^(-5))(3^(-1)Y^(-2))^-2 Thannkyou for your help. I tried distributing the -2 first and then keep coefficients and add exponents but i am lost.

Algebra ->  Exponents -> SOLUTION: (3^(-1)X^(3)Y^(-5))(3^(-1)Y^(-2))^-2 Thannkyou for your help. I tried distributing the -2 first and then keep coefficients and add exponents but i am lost.       Log On


   

Question 816550: (3^(-1)X^(3)Y^(-5))(3^(-1)Y^(-2))^-2
Thannkyou for your help. I tried distributing the -2 first and then keep coefficients and add exponents but i am lost.
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
%283%5E%28-1%29X%5E%283%29Y%5E%28-5%29%29%283%5E%28-1%29Y%5E%28-2%29%29%5E-2+
According to the order of operations (aka PEMDAS) we should start with the exponents (since nothing can be done within either set of parentheses). To raise the expression to the -2 power we use a rule for exponents, %28ab%29%5En+=+a%5En+%2A+b%5En, which tells us that raising a multiple-factor term to a power, you raise each factor to that power:

To raise the powers of a power we use another rule for exponents, %28a%5En%29%5Em+=+a%5E%28n%2Am%29:
%283%5E%28-1%29X%5E%283%29Y%5E%28-5%29%29%283%5E2%29%28Y%5E4%29+
All that is left is multiplying. For this we use another rule for exponents, a%5En+%2A+a%5Em+=+a%5E%28n%2Bm%29. We will use this on the 3's and the Y's:
3%5E%28%28-1%29%2B2%29X%5E%283%29Y%5E%28%28-5%29%2B4%29+
which simplifies to:
3%5E%281%29+X%5E%283%29Y%5E%28-1%29+
or
3x%5E3%2Fy

P.S. While the %28ab%29%5En+=+a%5En+%2A+b%5En property may look like a Distributive Property, it is not.