1. ## rational exponents

I need to simplify (49c^6)^(-5/2) down to 1/(343c^9) but I'm not sure how to do this. The same goes for (27a^3b^3)^(2/3). I find it much easier to simplify when they are in the form of x^a/n. Now, with all the new letters, i'm sort of confused. Any tips would be appreciated... thank you!

2. Originally Posted by ria3
I need to simplify (49c^6)^(-5/2) down to 1/(343c^9) but I'm not sure how to do this. ...
First: I assume that there is typo and you mean:

$\left(49c^6\right)^{-\frac32} = \left(7^2\right)^{-\frac32} \cdot \left(c^6\right)^{-\frac32} = 7^{-3} \cdot c^{-9} = \frac1{343c^9}$

In the attached pdf-file you'll find most of the rules concerning calculations of powers. Use it to do the other questions.