13.364. The base of the power was increased by $k$ times, and the exponent was decreased by the same factor, as a result of which the power itself did not change. Find the base of the power that has such a property.
## Solution.

Let $x, y$ be the base and the exponent. According to the condition, $(k x)_{k}^{\frac{y}{k}}=x^{y}$ or $(k x)_{k}^{\frac{1}{k}}=x$, from which $x=\sqrt[k-1]{k}$.

Answer: $\sqrt[k-1]{k}$