The expression \( \left(\frac{m^{2}}{m^{\frac{1}{3}}}\right)^{-\frac{1}{2}} \) is equivalent to

To simplify the expression \( \left(\frac{m^{2}}{m^{\frac{1}{3}}}\right)^{-\frac{1}{2}} \), we first can simplify the fraction inside the parentheses: \[ \frac{m^{2}}{m^{\frac{1}{3}}} = m^{2 - \frac{1}{3}} = m^{\frac{6}{3} - \frac{1}{3}} = m^{\frac{5}{3}}. \] Now, we raise this to the power of \(-\frac{1}{2}\): \[ \left(m^{\frac{5}{3}}\right)^{-\frac{1}{2}} = m^{\frac{5}{3} \cdot -\frac{1}{2}} = m^{-\frac{5}{6}}. \] The expression can also be simplified further by rewriting it with a positive exponent: \[ m^{-\frac{5}{6}} = \frac{1}{m^{\frac{5}{6}}}. \] Therefore, the expression \( \left(\frac{m^{2}}{m^{\frac{1}{3}}}\right)^{-\frac{1}{2}} \) is equivalent to \[ \frac{1}{m^{\frac{5}{6}}}. \]