[tex]Given : \frac{(x^\frac{2}{5})^9\;.\;(x^\frac{-4}{15})}{x^\frac{1}{3}}[/tex]
[tex]\implies {(x^\frac{18}{5})\;.\; (x^\frac{-4}{15})}\;.\;(x^\frac{-1}{3})[/tex]
[tex]\implies x^(^\frac{18}{5} ^-^\frac{4}{15}^-^\frac{1}{3}^)[/tex]
[tex]\implies x^(^(^\frac{54 - 4}{15}^)^-^\frac{1}{3}^) = x^(^(^\frac{50}{15}^)^-^\frac{1}{3}^) = x^(^(^\frac{10}{3}^)^-^\frac{1}{3}^) = x^(^\frac{9}{3}^) = x^3[/tex]
[tex]\implies x^k = x^3[/tex]
[tex]\implies k = 3[/tex]
