Write the following in simplified radical form. \[ \sqrt[5]{w^{13}} \] Assume that the variable represents a positive real number. \( \square \)

To simplify \( \sqrt[5]{w^{13}} \), we can break down the exponent. We know that \( w^{13} \) can be expressed as \( w^{10} \cdot w^3 \). Using the property of radicals, we can separate it: \[ \sqrt[5]{w^{13}} = \sqrt[5]{w^{10} \cdot w^3} = \sqrt[5]{w^{10}} \cdot \sqrt[5]{w^3} \] Now, since \( w^{10} = (w^2)^5 \), we have: \[ \sqrt[5]{w^{10}} = w^2 \] Now we handle \( \sqrt[5]{w^3} \), which we cannot simplify fully, so it remains as \( \sqrt[5]{w^3} \). Thus, putting it all together, we get: \[ \sqrt[5]{w^{13}} = w^2 \cdot \sqrt[5]{w^3} \] Finally, the simplified radical form is: \[ w^2 \sqrt[5]{w^3} \]