Question

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

choose all answers that apply:
a. (k^(-1))^(1/8)

b. (8_/`k)^(-1)

c. k^(-1/8)

d. none of the above


* _/` is a radical with 8 as the index and k as the radicand

Answer 1

The first option is correct: we have

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

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

`k^{(1)/(n)} = \sqrt[n]{k}`

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

`(a^b)^c = a^(bc)`