Question

select the equivalent expression. $sqrt6{k^{5} cdot k^{-1}}$ answer $k^{-\frac{2}{3}}$ $k^{\frac{1}{2}}$ $k^{\frac{2}{3}}$ $k^{-\frac{1}{2}}$

Explanation:

Step1: Combine exponents inside root

$k^5 \cdot k^{-1} = k^{5 + (-1)} = k^4$

Step2: Rewrite root as exponent

$\sqrt[6]{k^4} = k^{\frac{4}{6}}$

Step3: Simplify the exponent

$k^{\frac{4}{6}} = k^{\frac{2}{3}}$

Answer:

$k^{\frac{2}{3}}$ (the third option in the list)