Question 33386
{{{ 4^(3/4) }}}


this is either visualised as {{{ (4^3)^(1/4) }}} or as {{{ (4^(1/4))^3 }}}. The second is easier to work with, since {{{4^3}}} is a big number, whereas {{{4^(1/4)}}} is small...so easier, in my opinion.


{{{4^(1/4)}}} means what is the number "a" such that a*a*a*a=4? You should LEARN this sort of thing.


Hopefully you will know b if b*b=4? --> b is 2.
OK, so what about c*c=2? --> answer is {{{ c = sqrt(2) }}}


So, {{{ 4^(1/4) = sqrt(2) }}}


--> {{{ sqrt(2)*sqrt(2)*sqrt(2)*sqrt(2) = 4 }}}. Check it on your calculator.


So we have 
{{{ (4^(1/4))^3 }}}
{{{ (sqrt(2))^3 }}}
{{{ sqrt(2)*sqrt(2)*sqrt(2) }}}
{{{ 2sqrt(2) }}}


jon.