Giselle Moreno
Exponential Rules \( \omega \) / Fractions Level 2
May 14, 11:58:35 AM
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Select the equivalent expression.
\[
\left(\frac{k^{-2}}{k^{4}}\right)^{\frac{5}{14}}
\]
\( \frac{1}{\sqrt[15]{k^{7}}} \)
\( \sqrt[15]{k^{7}} \)
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\( \sqrt[7]{k^{15}} \)
\( \frac{1}{\sqrt[7]{k^{15}}} \)

Answer

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Answer

\( = k^{-\frac{30}{14}} = k^{-\frac{15}{7}} = \frac{1}{k^{\frac{15}{7}}} = \frac{1}{\sqrt[7]{k^{15}}} \)

Steps

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 ：\( = k^{-\frac{30}{14}} = k^{-\frac{15}{7}} = \frac{1}{k^{\frac{15}{7}}} = \frac{1}{\sqrt[7]{k^{15}}} \)