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In 1985, Restivo and Salemi presented a list of five problems concerningpower free languages. Problem $4$ states: Given $\alpha$-power-free words $u$and $v$, decide whether there is a transition from $u$ to $v$. Problem $5$states: Given $\alpha$-power-free words $u$ and $v$, find a transition word$w$, if it exists.  Let $\Sigma_k$ denote an alphabet with $k$ letters. Let $L_{k,\alpha}$ denotethe $\alpha$-power free language over the alphabet $\Sigma_k$, where $\alpha$is a rational number or a rational "number with $+$". If $\alpha$ is a "numberwith $+$" then suppose $k\geq 3$ and $\alpha\geq 2$. If $\alpha$ is "only" anumber then suppose $k=3$ and $\alpha>2$ or $k>3$ and $\alpha\geq 2$. We showthat: If $u\in L_{k,\alpha}$ is a right extendable word in $L_{k,\alpha}$ and$v\in L_{k,\alpha}$ is a left extendable word in $L_{k,\alpha}$ then there is a(transition) word $w$ such that $uwv\in L_{k,\alpha}$. We also show aconstruction of the word $w$.

Transition Property for $\alpha$-Power Free Languages with $\alpha\geq 2$ and $k\geq 3$ Letters