Simplify. Assume all variables are positive: \( \frac{\left(30 y^{\frac{1}{3}}\right)}{\left(5 y^{\frac{1}{2}}\right)} \) \( 6 y^{6} \) \( \frac{6}{y^{\frac{1}{6}}} \) \( \frac{y^{6}}{6} \) \( \frac{y^{\frac{1}{6}}}{6} \)

To simplify the expression \( \frac{\left(30 y^{\frac{1}{3}}\right)}{\left(5 y^{\frac{1}{2}}\right)} \), start by simplifying the numerical coefficients and the powers of \( y \). 1. Simplify the numbers: \( \frac{30}{5} = 6 \). 2. For the \( y \) terms: \( y^{\frac{1}{3}} \div y^{\frac{1}{2}} = y^{\frac{1}{3} - \frac{1}{2}} = y^{\frac{2}{6} - \frac{3}{6}} = y^{-\frac{1}{6}} \). Putting it all together, we get: \[ 6 y^{-\frac{1}{6}} = \frac{6}{y^{\frac{1}{6}}} \] So the simplified expression is \( \frac{6}{y^{\frac{1}{6}}} \).