SOLUTION: How do I solve this problem? I'm trying to help my daughter and I'm lost. 2a to the -5 power over b to the -6 power. She is trying to simplify this problem.

Algebra ->  Exponents-negative-and-fractional -> SOLUTION: How do I solve this problem? I'm trying to help my daughter and I'm lost. 2a to the -5 power over b to the -6 power. She is trying to simplify this problem.      Log On


   

Question 724815: How do I solve this problem? I'm trying to help my daughter and I'm lost.
2a to the -5 power over b to the -6 power.
She is trying to simplify this problem.
Found 2 solutions by KMST, mananth:
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
I would not call it simplifying, but we can transform it into an expression with positive exponents:
2a%5E%28-5%29%2Fb%5E%28-6%29=2b%5E6%2Fa%5E5
Any powers with negative exponents can cross the fraction line to make their exponents turn positive.

EXPLANATION:
a%5E%28-5%29=1%2Fa%5E5 by definition, and b%5E%28-6%29=1%2Fb%5E6 too
b%5E%28-6%29=1%2Fb%5E6 <---> b%5E%28-6%29%2Ab%5E6=1 <---> b%5E6=1%2Fb%5E%28-6%29
In baby steps that are not usually spelled out:

Answer by mananth(16946) About Me  (Show Source):