SOLUTION: I need help doing 81^-3/4 without a calculator, the part stumping me is how to do {{{4sqrt(81^3)}}} is it possible for a step by step explanation on how to solve

Algebra ->  Square-cubic-other-roots -> SOLUTION: I need help doing 81^-3/4 without a calculator, the part stumping me is how to do {{{4sqrt(81^3)}}} is it possible for a step by step explanation on how to solve      Log On


   

Question 781020: I need help doing 81^-3/4 without a calculator, the part stumping me is how to do
4sqrt%2881%5E3%29 is it possible for a step by step explanation on how to solve
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The order of the operations makes a big difference
+81%5E%28-3%2F4%29+
Think of this as:
+1%2F%28+root%28+4%2C81+%29%29%5E3+
Note that +81+=+3%2A3%2A3%2A3+, so
+81+=+3%5E4+ and
+root%28+4%2C3%5E4+%29+=+3+, so
+1%2F3%5E3+=+1%2F27+
----------------------
check:
+81%5E%28-3%2F4%29++=+1%2F27+
+81%5E%28-3%2F4%29++=+1%2F3%5E3+
+%283%5E4%29%5E%28-3%2F4%29+=+3%5E%28-3%29+
+3%5E%28-3%29+=+3%5E%28-3%29+
OK