SOLUTION: Write cube route of 16 in the form 2 to the k, k E Q

Algebra ->  Square-cubic-other-roots -> SOLUTION: Write cube route of 16 in the form 2 to the k, k E Q      Log On


   

Question 223222: Write cube route of 16 in the form 2 to the k, k E Q
Found 2 solutions by jim_thompson5910, Edwin McCravy:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
root%283%2C16%29=root%283%2C2%5E4%29=%282%5E4%29%5E%281%2F3%29=2%5E%284%2F3%29%5E%22%22. So in this case, k=4%2F3

Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
Write root%283%2C16%29 in the form 2%5Ek, k∊Q

Use the rule: root%28n%2Cx%29=x%5E%281%2Fn%29

root%283%2C16%29=16%5E%281%2F3%29

Now use the fact that 16=2%5E4,

root%283%2C16%29=16%5E%281%2F3%29=%282%5E4%29%5E%281%2F3%29

Use the rule that %28x%5Em%29%5En=x%5E%28mn%29

root%283%2C16%29=16%5E%281%2F3%29=%282%5E4%29%5E%281%2F3%29=2%5E%284%2F3%29

Edwin