Question

Which expression is equivalent to StartFraction a Superscript StartFraction 2 over 3 EndFraction Baseline over b Superscript StartFraction 1 over 3 EndFraction Baseline EndFraction plus StartFraction b Superscript StartFraction 2 over 3 EndFraction Baseline over a Superscript StartFraction 1 over 3 EndFraction Baseline EndFraction?

Answer options with 5 options
A.
StartFraction a plus b over a Superscript StartFraction 1 over 3 EndFraction Baseline b Superscript StartFraction 1 over 3 EndFraction Baseline EndFraction

B.
StartFraction a Superscript StartFraction 2 over 3 EndFraction Baseline plus b Superscript StartFraction 2 over 3 EndFraction Baseline over a Superscript StartFraction 1 over 3 EndFraction Baseline plus b Superscript StartFraction 1 over 3 EndFraction Baseline EndFraction

C.
StartFraction a plus b over a Superscript StartFraction 1 over 3 EndFraction Baseline plus b Superscript StartFraction 1 over 3 EndFraction Baseline EndFraction

D.
StartFraction a Superscript StartFraction 2 over 9 EndFraction Baseline plus b Superscript StartFraction 2 over 9 EndFraction Baseline over a Superscript StartFraction 1 over 3 EndFraction Baseline b Superscript StartFraction 1 over 3 EndFraction Baseline EndFraction

E.
StartFraction a Superscript StartFraction 2 over 3 EndFraction Baseline b Superscript StartFraction 1 over 3 EndFraction Baseline plus a Superscript StartFraction 1 over 3 EndFraction Baseline b Superscript StartFraction 2 over 3 EndFraction Baseline over a Superscript StartFraction 1 over 3 EndFraction Baseline b Superscript 1 over 3 Baseline EndFraction

Answer 1

Let x = a^(1/3) and y = b^(1/3). Then the expression is x^2/y + y^2/x = (x^3 + y^3)/(xy) = (a + b)/(a^(1/3) b^(1/3)).

So the correct choice is A.