The given expression is:

$\frac{1}{\sqrt{7}}$

We want to simplify this expression. One way to simplify such an expression is to rationalize the denominator. To do this, we multiply both the numerator and denominator by $\sqrt{7}$:

$\frac{1}{\sqrt{7}} \times \frac{\sqrt{7}}{\sqrt{7}} = \frac{\sqrt{7}}{7}$

This gives the simplified form:

$\frac{\sqrt{7}}{7}$

Looking at the answer choices:

a) $\frac{\sqrt{7}}{7}$
b) $\frac{1}{\sqrt{49}}$
c) $\frac{1}{7}$
d) $7$

The correct answer is a) $\frac{\sqrt{7}}{7}$.

Would you like more details on this solution or have any further questions?

Here are five related questions to practice:

1. How would you simplify $\frac{1}{\sqrt{3}}$?
2. What is $\frac{\sqrt{2}}{2}$ simplified from $\frac{1}{\sqrt{2}}$?
3. How can you rationalize $\frac{1}{\sqrt{11}}$?
4. What happens if you multiply $\frac{1}{\sqrt{x}}$ by $\sqrt{x}$?
5. How does rationalizing the denominator help in simplifying expressions?

Tip: Rationalizing the denominator means removing the square root from the denominator by multiplying both the numerator and denominator by the same square root.