Fractional Exponents outside ()

[headacheinalgebra]

Will someone please try to explain how to work such a problem? The exponents in fractional form outside the (_) are very confusing to me. Thank you very much.

8b^9c^5
______
27b^-3c^-9

This problem is enclosed by one set of () and has an exponent of ^1/3. I am asked to simplify with variables to represent positive numbers.

 

[Loren]

\(\displaystyle (\frac{8b^9c^5}{27b^{-3}c^{-9}})^{-\frac{1}{3}\)

Probably your best bet is to apply the rule of exponents that says \(\displaystyle (x^ay^b)^n=x^{an}y^{bn}\) first. Then use the other rules of exponents in any order you desire. I would probably apply the following next--- \(\displaystyle a^{-n}=\frac{1}{a^n}\) and \(\displaystyle \frac{1}{a^{-n}}= a^n\). Then I would use whatever I need to get all the factors in the numerator or all exponents being positive, whichever the instructions had indicated.