SOLUTION: If m and p are positive integers and (2√2)^m = 32^p, what is the value of p/m ?

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: If m and p are positive integers and (2√2)^m = 32^p, what is the value of p/m ?      Log On


   

Question 1105179: If m and p are positive integers and (2√2)^m = 32^p, what is the value of p/m ?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
If m and p are positive integers and (2√2)^m = 32^p,
what is the value of p/m?
:
%282sqrt%282%29%29%5Em+=+32%5Ep
we can write both sides as power of 2
:
2%5E%28%283m%29%2F2%29 = 2%5E%285p%29; that's 3m/2
therefore
%283m%29%2F2 = 5p
multiply both sides by 2
3m = 10p
"What is the value of p/m"
p%2Fm = 3%2F10
:
:
Check this with original equation, replacing m and p, use a calc
%282sqrt%282%29%29%5E10 = 32%5E3
32768 = 32768