Simplify. \( \frac{\sqrt[10]{x^{7}}}{\sqrt[7]{x^{2}}} \) \( x^{[?]} \)

To simplify \( \frac{\sqrt[10]{x^{7}}}{\sqrt[7]{x^{2}}} \), we start by rewriting the radicals using exponents: The numerator becomes \( x^{7/10} \) and the denominator becomes \( x^{2/7} \). Therefore, we have: \[ \frac{x^{7/10}}{x^{2/7}} = x^{7/10 - 2/7} \] Now, let's find a common denominator for the exponents: The least common multiple of 10 and 7 is 70. Now we convert the fractions: - \( \frac{7}{10} = \frac{49}{70} \) - \( \frac{2}{7} = \frac{20}{70} \) Thus, we can now subtract the exponents: \[ \frac{49}{70} - \frac{20}{70} = \frac{29}{70} \] So we have: \[ x^{7/10 - 2/7} = x^{29/70} \] The simplified form is \( x^{\frac{29}{70}} \).