# A "New" Operation

Algebra Level 3

To every pair of positive real numbers $$x$$ and $$y$$, we assign a positive real number $$x\star y$$ satisfying the two properties that $$x\star x=1$$ and $$x\star (y\star z)=(x\star y) \times z$$ (where $$\times$$ represents standard multiplication). Find $$k$$ if $$61\star 2013=\frac{1}{k}$$.

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