Simplify the expression by converting to rational exponents. Assume that all variables represent posilive real numbers. \( \frac{\sqrt[3]{t^{2}}}{\sqrt[5]{t^{2}}} \) \( \frac{\sqrt[3]{t^{2}}}{\sqrt[5]{t^{2}}}=\square \) (Type an exact answer.)

To simplify the expression \( \frac{\sqrt[3]{t^{2}}}{\sqrt[5]{t^{2}}} \), we first convert the roots to rational exponents. This gives us \( \frac{t^{2/3}}{t^{2/5}} \). Now, to simplify this fraction, we can subtract the exponents of \( t \): \[ t^{2/3 - 2/5}. \] To subtract the fractions, we need a common denominator, which in this case is 15. Therefore, we rewrite the fractions: \[ 2/3 = 10/15 \quad \text{and} \quad 2/5 = 6/15. \] Now we can perform the subtraction: \[ \frac{10}{15} - \frac{6}{15} = \frac{4}{15}. \] Thus, we have: \[ t^{2/3 - 2/5} = t^{4/15}. \] Finally, the simplified expression is: \[ \frac{\sqrt[3]{t^{2}}}{\sqrt[5]{t^{2}}} = t^{4/15}. \] So, the answer is \( t^{\frac{4}{15}} \) or just: \( \frac{\sqrt[3]{t^{2}}}{\sqrt[5]{t^{2}}} = t^{\frac{4}{15}} \).