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The number of rational terms in the expansion of ${(5^{1 / 6} + 7^{1 / 9})}^{1824}$ is _____

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answer is 102.

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Detailed Solution

$T_{r + 1} = 1824 c_{r} 5 \frac{1824 - r}{6} 7^{\frac{r}{9}}$

For rational terms $1824 - r = 6 k$ & $r = 9 k$
The $[\frac{1824}{18}] + 1 = 102$ rational terms.

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