[tex]\dfrac{1}{ \left(\sqrt[3] 7 \right)^5} = 7^n\\\\\\\implies \left(\sqrt[3] 7 \right)^{-5} = 7^n\\\\\\\implies \left(7^{\tfrac 13} \right)^{-5} =7^n\\\\\\\implies 7^{-\tfrac 53} = 7^n\\\\\\ \implies n = -\dfrac 53[/tex]
