Finding the Greatest Value: Mathematical Comparison Exercise

To determine if one of these values is the largest or if they are equal, we will express each expression as a power of 5:

• First, consider $\sqrt[6]{\sqrt{5}}$. This is equivalent to $(\sqrt{5})^{1/6} = (5^{1/2})^{1/6}$. Applying the power rule, this is $5^{1/12}$.
• Next, consider $\sqrt[12]{5}$, which is already expressed as a power: $5^{1/12}$.
• Finally, consider $\sqrt[4]{\sqrt[3]{5}}$. This can be rewritten as $(\sqrt[3]{5})^{1/4} = (5^{1/3})^{1/4}$. Again, using the power rule, this is $5^{1/12}$.

All three expressions simplify to $5^{1/12}$. Therefore, all values are equal. The correct choice is:

All values are equal.