If ${\left(x^{-2}\right)}^3=\frac{1}{x^k}$, then find the value of $k$.

If $\frac{x^{-3}}{x^{-4}}=x^k$, then find the value of $k$.

If $\frac{x^{-2}}{x^3}=x^k$, then find the value of $k$.

Evaluate:

$8^{\frac{1}{3}}$

Evaluate:

${32}^{\frac{1}{5}}$

Evaluate:

$8^{\frac{4}{3}}$

Evaluate:

${216}^{\frac{2}{3}}$

Evaluate:

${256}^{0.75}$

On simplifying $x^{\frac{1}{3 }}\times x^{\frac{1}{3}}$ we get ${\left(\sqrt[k]{x}\right)}^2$. Find the value of $k$.