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If the exponential form of the surd $\sqrt{2}$ is $2^k$, then find the value of $k$.

If the surd $\sqrt[3]{9}$ can be expressed in exponential form as $9^k$, then find the value of $k$.

If the exponential form of the surd $\sqrt[5]{20}$ is in the form $k^{\frac{1}{m}}$, then find the value of $k+m$.

If the surd$\sqrt[17]{19}$ can be expressed in exponential form as ${19}^k$, then find the value of $k$.

If the radical form of $5^{\frac{1}{7}}$ is $\sqrt[n]{5}$, then the value of $n$ is

If the surds ${17}^{\frac{1}{6}}$ is in radical form as $\sqrt[m]{k}$, then find the value of $\left(k+m\right)$.

If the surds $5^{\frac{2}{5}}$ is of radical form as as $\sqrt[m]{k}$, then find the value of $\left(k+m\right)$, where $k$ and $m$ are integers.

If the surds ${142}^{\frac{1}{2}}$ is in radical form as $\sqrt[m]{k}$, then find the value of $\left(k+m\right)$.