\( 1 \leftarrow \frac{\sqrt[3]{t^{2}}}{\sqrt[6]{t^{2}}} \) Simplify the expression by converting to rational exponents. Assume that all variables represent positive real numbers. \( \quad \begin{array}{l}\frac{\sqrt[3]{t^{2}}}{\sqrt[6]{t^{2}}}=\square \\ \text { (Type an exact answer.) }\end{array} \)

To simplify the expression \( \frac{\sqrt[3]{t^{2}}}{\sqrt[6]{t^{2}}} \), we first rewrite the radicals in terms of rational exponents. We have: \[ \sqrt[3]{t^2} = t^{2/3} \quad \text{and} \quad \sqrt[6]{t^2} = t^{2/6} = t^{1/3}. \] Now substituting these into the original expression, we get: \[ \frac{t^{2/3}}{t^{1/3}}. \] Using the property of exponents that states \( \frac{a^m}{a^n} = a^{m-n} \), we simplify this to: \[ t^{2/3 - 1/3} = t^{1/3}. \] Therefore, the simplified expression is: \[ \frac{\sqrt[3]{t^{2}}}{\sqrt[6]{t^{2}}} = t^{1/3}. \]