Question 824765
Good try!
I often have trouble showing fractional exponents too.
When in trouble, putting the fractions in quotation marks sort of makes it readable, like this:
{{{4a^(-"1/2")  (a^"5/2" - a^(-"3/2"))}}}
 
{{{4a^(-"1/2")(a^"5/2"-a^(-"3/2"))=4a^(-"1/2")*a^"5/2"-4a^(-"1/2")*a^(-"3/2")=
4a^(-"1/2+5/2")-4a^(-"1/2-3/2")=4a^2-4a^(-2)=highlight(4a^2-4/a^2)}}}
 
NOTE:
I am not sure that {{{4a^2-4/a^2}}} would be considered "simplified".
Simplicity is in the eye of the beholder.
Maybe
{{{4(a^2-1/a^2)}}} ,
or {{{4(a^4-1)/a^2}}} ,
or {{{4(a^2+1)(a+1)(a-1)/a^2}}}
would be preferred.