SOLUTION: Short Answer: Simplify the following expression, and rewrite it in an equivalent form with positive exponents. {{{(-6x^-5)^-2}}} Any help would be greatly appreciated!

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Short Answer: Simplify the following expression, and rewrite it in an equivalent form with positive exponents. {{{(-6x^-5)^-2}}} Any help would be greatly appreciated!      Log On


   

Question 373650: Short Answer: Simplify the following expression, and rewrite it in an equivalent form with positive exponents.
%28-6x%5E-5%29%5E-2
Any help would be greatly appreciated!
Found 2 solutions by jsmallt9, josmiceli:
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
%28-6x%5E-5%29%5E-2
First we will simplify. Then we will deal with negative exponents, if any are left.

To simplify this we will be using the rule: %28a%2Ab%29%5Eq+=+a%5Eq%2Ab%5Eq:
%28-6%29%5E%28-2%29%28x%5E%28-5%29%29%5E%28-2%29
For %28x%5E%28-5%29%29%5E%28-2%29 we will use the rule: %28a%5Ep%29%5Eq+=+a%5E%28p%2Aq%29:
%28-6%29%5E%28-2%29x%5E%28%28-5%29%2A%28-2%29%29
which simplifies to:
%28-6%29%5E%28-2%29%2Ax%5E10
Now we will eliminate the negative exponent on the -6. For this we will use the rule: a%5E%28-q%29+=+1%2Fa%5Eq. This gives us:
%281%2F%28-6%29%5E2%29%2Ax%5E10
Since %28-6%29%5E2+=+36 this becomes:
%281%2F36%29%2Ax%5E10
which simplifies to:
x%5E10%2F36
This is the simplified expression with positive exponents.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
I usually start with the inside and work my way out
%28-6%2Ax%5E%28-5%29%29%5E%28-2%29
%28-6%2A%281%2Fx%5E5%29%29%5E%28-2%29
%28-6%2Fx%5E5%29%5E%28-2%29
%28-x%5E5%2F6%29%5E2
x%5E10%2F36
The general rule I used here is
%28a%2Fb%29%5E%28-c%29+=+%281%2F%28a%2Fb%29%29%5Ec
%281%2F%28a%2Fb%29%29%5Ec+=+%28b%2Fa%29%5Ec