1. The problem is to verify or simplify the expression $$\sqrt{5} \sqrt[5]{5}$$ and compare it to $$5^{\frac{2}{7}}$$. 2. Recall the rules for exponents and radicals: - The square root of a number is the same as raising it to the power of $\frac{1}{2}$. - The fifth root of a number is the same as raising it to the power of $\frac{1}{5}$. - When multiplying powers with the same base, add the exponents: $$a^m \times a^n = a^{m+n}$$. 3. Rewrite the expression using exponents: $$\sqrt{5} = 5^{\frac{1}{2}}$$ $$\sqrt[5]{5} = 5^{\frac{1}{5}}$$ 4. Multiply the two expressions: $$5^{\frac{1}{2}} \times 5^{\frac{1}{5}} = 5^{\frac{1}{2} + \frac{1}{5}}$$ 5. Find a common denominator and add the exponents: $$\frac{1}{2} = \frac{5}{10}, \quad \frac{1}{5} = \frac{2}{10}$$ $$\frac{5}{10} + \frac{2}{10} = \frac{7}{10}$$ 6. So the expression simplifies to: $$5^{\frac{7}{10}}$$ 7. Compare this to the given expression $$5^{\frac{2}{7}}$$. 8. Since $$\frac{7}{10} \neq \frac{2}{7}$$, the original expression $$\sqrt{5} \sqrt[5]{5}$$ is not equal to $$5^{\frac{2}{7}}$$. Final answer: $$\sqrt{5} \sqrt[5]{5} = 5^{\frac{7}{10}} \neq 5^{\frac{2}{7}}$$.