Question 759755
given:

{{{2^(5/2)-2^(3/2)}}}
 
clarification on this part: {{{2^(3/2)*2^(2/2) - 2^3/2}}}

if you have {{{2^(5/2)}}} you can write exponent {{{(5/2)}}} as {{{(3/2+2/2)}}}, then you have  {{{2^(5/2)=2^(3/2+2/2)}}}, then you use multiplication rule and write {{{ 2^(3/2+2/2)}}} as a product like this {{{2^(3/2)*2^(2/2)}}}

now back to {{{2^(3/2)*2^(2/2) - 2^(3/2)}}}...factor

{{{2^(3/2)(2^(2/2) - 1)}}}....write {{{2^(2/2)}}} as {{{sqrt(2^2)}}} and you see that is equal {{{2}}} 

{{{2^(3/2)(2 - 1)}}}

{{{2^(3/2)*1}}}

{{{2^(3/2)}}}

{{{sqrt(2^3)}}}

{{{2sqrt(2)}}}......simple form

{{{2*1.41}}}

{{{2.82}}}...final result