Problem
Select the equivalent expression. \[ \sqrt[15]{\frac{1}{s^{6} \cdot s^{4}}} \] \( s^{-\frac{3}{2}} \) \( s^{\frac{2}{3}} \) Submit Answer \( s^{\frac{3}{2}} \) \( s^{-\frac{2}{3}} \)
Solution
Step 1 ：Combine exponents in the denominator: \(\frac{1}{s^{6}\cdot s^{4}} = \frac{1}{s^{(6+4)}} = \frac{1}{s^{10}}\)
Step 2 ：Rewrite the fraction as a negative exponent: \(\frac{1}{s^{10}} = s^{-10}\)
Step 3 ：Apply the 15th root: \(\sqrt[15]{s^{-10}} = s^{\frac{-10}{15}} = s^{\frac{-2}{3}}\)
