Expressing the following number "Sixth root of $9$" in index form gives $9^x$. Find the value of $x$.

The index form of square root of $256$is ${256}^{\frac{1}{k}}$, find the value of $k$.

The cube root of $17$ in index form is${17}^{\frac{1}{k}}$, what is the value of $k$.

Index form of eighth root of $100$is ${100}^{\frac{1}{k}}$, find the value of $k$

Expressing the following number "Seventh root of $30$" in index form gives ${30}^x$. Find the value of $x$.

Write in the form '${\mathrm{n}}^{\mathrm{th}}$ root of $\mathrm{a}$' of the given number. 

${\left(81\right)}^{\frac{1}{4}}$

Write in the form '${\mathrm{n}}^{\mathrm{th}}$ root of $\mathrm{a}$' of the given number. 

$(49{)}^{\frac{1}{2}}$

Write in the form '${\mathrm{n}}^{\mathrm{th}}$ root of $\mathrm{a}$' of the given number. 

${\left(15\right)}^{\frac{1}{5}}$

Write in the form '${\mathrm{n}}^{\mathrm{th}}$ root of $\mathrm{a}$' of the given number. 

 ${\left(512\right)}^{\frac{1}{9}}$