SOLUTION: Please note, am NOT seeking answer to following problem (already know it), just have a question regarding the properties to evaluate correctly. Problem: (8/27)^-(2/3) 1) rewrit

Algebra ->  Radicals -> SOLUTION: Please note, am NOT seeking answer to following problem (already know it), just have a question regarding the properties to evaluate correctly. Problem: (8/27)^-(2/3) 1) rewrit      Log On


   

Question 874057: Please note, am NOT seeking answer to following problem (already know it), just have a question regarding the properties to evaluate correctly.
Problem: (8/27)^-(2/3)
1) rewrite as 1/(8/27)^(2/3)
2) rewrite as 1/(thirdroot(8/27))^2
If above is correct so far, here's my question:
why would it be incorrect to write 1/(thirdroot((8/27)^2)?

Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
let's begin with rewriting step 2
2) 1 / (8/27)^(2/3)
3) 1 / (2^3 / 3^3)^2/3
now we can multiply the exponents
4) 1 / (2^2 / 3^2)
5) 1 / (4/9)
6) 9/4 = 2.25