1. **Stating the problem:** We need to verify which of the given options is equal to $$\frac{\sqrt[3]{a}}{\sqrt{a}}$$. 2. **Recall the rules for roots and exponents:** - The $n$-th root of $a$ can be written as $a^{\frac{1}{n}}$. - The square root $\sqrt{a} = a^{\frac{1}{2}}$. - When dividing powers with the same base, subtract the exponents: $a^m / a^n = a^{m-n}$. 3. **Rewrite the expression using exponents:** $$\frac{\sqrt[3]{a}}{\sqrt{a}} = \frac{a^{\frac{1}{3}}}{a^{\frac{1}{2}}} = a^{\frac{1}{3} - \frac{1}{2}}$$ 4. **Calculate the exponent difference:** $$\frac{1}{3} - \frac{1}{2} = \frac{2}{6} - \frac{3}{6} = -\frac{1}{6}$$ 5. **Simplify the expression:** $$a^{-\frac{1}{6}} = \frac{1}{a^{\frac{1}{6}}} = \frac{1}{\sqrt[6]{a}}$$ 6. **Compare with the options:** - a) $\sqrt{a} = a^{\frac{1}{2}}$ - b) $\sqrt[4]{a} = a^{\frac{1}{4}}$ - c) $\sqrt[6]{a} = a^{\frac{1}{6}}$ - d) $\sqrt[13]{a} = a^{\frac{1}{13}}$ Our expression equals $\frac{1}{\sqrt[6]{a}}$, which is the reciprocal of option c). **Final answer:** None of the options exactly equal $$\frac{\sqrt[3]{a}}{\sqrt{a}}$$, but it is equal to the reciprocal of option c) $\sqrt[6]{a}$. If the question implies equality without reciprocal, none match exactly.