SOLUTION: Can anyone please help with this rational exponents problem? Simplify using the rules of exponents and give detailed step by step directions on how you arrive to the solution.

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Question 862109: Can anyone please help with this rational exponents problem?
Simplify using the rules of exponents and give detailed step by step directions on how you arrive to the solution.
27^(-2/3)/27^(-1/3)
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Both exponents start as negative; and there is a rule like, b%5E%28-a%29=1%2Fb%5Ea.
Not really the best rule to most immediately use. Notice both bases are 27. Also is the exponent rule like %28b%5Ea%29%2Fb%5Ec=b%5E%28a-c%29, more useful here.
27%5E%28-2%2F3%29%2F27%5E%28-1%2F3%29
27%5E%28-2%2F3-%28-1%2F3%29%29
27%5E%281%2F3-2%2F3%29
27%5E%28-1%2F3%29
and NOW you can use the first stated rule about the negative exponents:
WAIT. Not really necessary. WHY?

%283%5E3%29%5E%28-1%2F3%29, simply factored the base;
Know THIS rule: %28b%5Ea%29%5Ec=b%5E%28ac%29

Next step then is
3%5E%283%28-1%2F3%29%29
3%5E%28-1%29
highlight%28%281%2F3%29%29

One big problem on the site is that rendering of rational exponents often works badly. write me a message if you want to see the steps through a different form or platform.