Answer
$\frac{1}{k^{2}}$
Work Step by Step
According to the power rule for exponents, $(a^{m})^{n}=a^{mn}$ (where $m$ and $n$ are integers and $a$ is a real number).
Therefore, $(k^{2})^{-3}k^{4}=k^{2\times-3}k^{4}=k^{-6}k^{4}$.
According to the product rule for exponents, $a^{m}\times a^{n}=a^{m+n}$.
Therefore, $k^{-6}k^{4}=k^{-6+4}=k^{-2}$.
According to the negative definition for exponents, $a^{-n}=\frac{1}{a^{n}}$ (where $a\ne0$).
Therefore, $k^{-2}=\frac{1}{k^{2}}$.