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Math·Advanced Math·Equivalent expressions

hard

$(x^{9k})\cdot \sqrt[3]{x^{13}}$, where $k$ is a constant and $x>0$, is equivalent to $\frac{\sqrt[5]{x}}{x^5}$. What is the value of $k$?

A

$\frac{5}{13}$

B

$\frac{24}{5}$

C

$-\frac{135}{137}$

D

$-\frac{137}{135}$