Simplify. \( \sqrt{x^{13}} \) Assume that the variable represents a positive real

To simplify \( \sqrt{x^{13}} \), we can use the property of square roots that states \( \sqrt{a^b} = a^{b/2} \). Applying this here gives us: \[ \sqrt{x^{13}} = x^{13/2} \] Since \( 13/2 \) can be expressed as \( 6.5 \), we have: \[ x^{13/2} = x^{6.5} = x^6 \cdot x^{0.5} = x^6 \sqrt{x} \] Thus, the simplified form is: \[ x^6 \sqrt{x} \] So, \( \sqrt{x^{13}} = x^6 \sqrt{x} \) is the final answer.