Question 31240
{{{ (8)^2/3}}} means either {{{ (8^2)^(1/3) }}} or {{{ (8^(1/3))^2 }}}. You can solve either. However, the first version has {{{8^2}}} which is 64 then we need to find a cube root of that etc... Going the way of "increasing the numbers" is more difficult.


My approach would always be to do the fractional power first if possible, to keep the numbers smaller:
{{{ (8^(1/3))^2 }}}

since 2*2*2 = 8
--> {{{ 2^2 }}}
--> 4


{{{(16)^1/4}}} means what number multplied to itself 4 times is 16? Answer is 2:
2*2*2*2 = 16


You need to recognise the following, in relation to powers:


2: 2,4,8,16,32,64,128,256,512,1024
3: 3,9,27,81
4: 4,16,64
5: 5,25,125,625
6: 6,36,216
7: 7,49,343
8: 8,64,512
9: 9,81,729


Recognise these numbers at least. Learn them if possible. That way you can answer the following type of Q really confidently:


{{{ 343^(2/3) }}} means {{{ (343^(1/3))^2 }}} --> {{{ 7^2 }}} --> 49


jon.