Prove if $\omega$ = $\beta^{-1}$ ($a_{1}$,...,$a_{k}$) $\beta$ then $\omega$ = ($\beta^{-1}$($a_{1}$),...,$\beta^{-1}$($a_{k}$))

Question

Let ($a_{1}$,...,$a_{k}$) be a cycle of length $k$. Prove if $\omega$ = $\beta^{-1}$ ($a_{1}$,...,$a_{k}$) $\beta$ then $\omega$ = ($\beta^{-1}$($a_{1}$),...,$\beta^{-1}$($a_{k}$))

I know that $\beta^{-1}$ = ($a_{k}$,...,$a_{1}$)