Question 1105179
If m and p are positive integers and (2√2)^m = 32^p,
 what is the value of p/m? 
:
{{{(2sqrt(2))^m = 32^p}}}
we can write both sides as power of 2
:
{{{2^((3m)/2)}}} = {{{2^(5p)}}}; that's 3m/2
therefore
{{{(3m)/2}}} = {{{5p}}}
multiply both sides by 2
3m = 10p
"What is the value of p/m"
{{{p/m}}} = {{{3/10}}}
:
:
Check this with original equation, replacing m and p, use a calc
{{{(2sqrt(2))^10}}} = {{{32^3}}}
32768 = 32768