Question

Which expressions are equivalent to (k^(1/8))^(−1) ?

Answer 1

The first option is correct: we have

$\left(k^{\frac{1}{8}}\right)^{-1} = \dfrac{1}{k^{\frac{1}{8}}} = \dfrac{1}{\sqrt[8]{k}},\quad \left(k^{-1}\right)^{\frac{1}{8}} = \left(\dfrac{1}{k}\right)^{\frac{1}{8}} = \dfrac{1}{\sqrt[8]{k}}$

The second option is also correct, because it simply applies the definition

$k^{\frac{1}{n}} = \sqrt[n]{k}$

The third option is also correct, because it applies the rule

$(a^b)^c = a^{bc}$