Question 125678
You want to express {{{1/sqrt(x)}}} as {{{x^b}}}, so we need to find an appropriate value for b.


First thing to realize is that {{{1/a^m=a^(-m)}}}, and the second thing is that {{{root(n,a)=a^(1/n)}}}


Applying both of these rules, {{{b=-1/2}}}, so your index form is {{{x^(-1/2)}}}


I think your second problem looks like this {{{(sqrt(x^5))^4}}}.  Using {{{root(n,a)=a^(1/n)}}} again, we can say {{{(sqrt(x^5))^4=((x^5)^(1/2))^4}}}.


Now we need another rule to apply:  {{{(a^m)^n=a^mn}}} 


Since {{{5*(1/2)*4=10}}}, your index form becomes {{{x^10}}}