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I am stumped as to why this application of the difference of cubes is valid... I am rationalizing the denominator. I don't understand the reasoning of why the difference of cubes formula is applicable to cubed roots, removing the root one gets an exponent of $a^{1/3}$ - I know how to simplify this expression, but I am hoping someone can help me along with the logic.

$$\frac{1}{\sqrt[3]{a}-\sqrt[3]{b}}.$$

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    We have $x^3-y^3=(x-y)(x^2+xy+y^2)$. Let $x=\sqrt[3]{a}$ and $y=\sqrt[3]{b}$.2012-04-17

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