Problem
Giselle Moreno Exponential Rules \( \omega \) / Fractions Level 2 May 14, 11:58:35 AM Watch help video Select the equivalent expression. \[ \left(\frac{k^{-2}}{k^{4}}\right)^{\frac{5}{14}} \] \( \frac{1}{\sqrt[15]{k^{7}}} \) \( \sqrt[15]{k^{7}} \) Submit Answer \( \sqrt[7]{k^{15}} \) \( \frac{1}{\sqrt[7]{k^{15}}} \)
Solution
Step 1 ：\( \left(\frac{k^{-2}}{k^{4}}\right)^{\frac{5}{14}} = \left(\frac{1}{k^6}\right)^{\frac{5}{14}} \)
Step 2 ：\( = \left(k^{-6}\right)^{\frac{5}{14}} \)
Step 3 ：\( = k^{-\frac{30}{14}} = k^{-\frac{15}{7}} = \frac{1}{k^{\frac{15}{7}}} = \frac{1}{\sqrt[7]{k^{15}}} \)
