And that is why parentheses (or better yet mathematical formatting with tools like latex) are used. It would have been much better if the original formula was expressed as .
Also, note the spacing in the original formula. a multiplication is set off by spaces on either side. Wouldn't division (if that was intended) be similarly set off, like 2/3 * (2)^2 / 3 = 4/3 * root 2? My guess is by NOT using the extra spaces, the originator was attempting to indicate what was likely shown as a fraction in his text. Yes fractions are division and you do execute the order of operations correctly, but a better use of the forum would be to answer the problem as intended (and then point out the error), rather than critique formatting.
Plus the subject line states clearly that the problem concerns fractional exponents!
WARNING: Beer soaked rambling/opinion/observation/reckoning ahead. Would be readers can take it seriously or take it with a grain of salt. In no event shall the wandering quixotic math knight-errant Sir jonah in his inebriated state (usually in his dead tired but mentally revived inebriated state) be liable to anyone for special, collateral, incidental, or consequential damages in connection with or arising out of the use of his "enhanced" beer (and tequila/absinthe) powered views.
Your contribution, late as it, is still very much appreciated.
Especially appreciated was my old friend Sir Denis' delightful caffeine soaked arguments roughly 5 or 6 years ago.