The problem provided asks to simplify the expression $\frac{1}{a^{5/8}}$.

To simplify:

$\frac{1}{a^{5/8}} = a^{-5/8}$

Now, we need to match this with one of the provided answer choices. Let's inspect them:

1. $\frac{\sqrt[8]{a^5}}{a}$
2. $\frac{\sqrt[8]{a^3}}{a}$
3. $\frac{a^{3/8}}{a}$

Let's analyze each option:

1. $\frac{\sqrt[8]{a^5}}{a} = \frac{a^{5/8}}{a} = a^{5/8 - 1} = a^{-3/8}$
2. $\frac{\sqrt[8]{a^3}}{a} = \frac{a^{3/8}}{a} = a^{3/8 - 1} = a^{-5/8}$
3. $\frac{a^{3/8}}{a} = a^{3/8 - 1} = a^{-5/8}$

Thus, the correct answer is Option 2: $\frac{\sqrt[8]{a^3}}{a}$.

Would you like further details or have any other questions? Here are five related questions:

1. How do you simplify expressions with fractional exponents?
2. What is the general rule for dividing exponents with the same base?
3. Can you explain the difference between $a^{m/n}$ and $\sqrt[n]{a^m}$?
4. How do you convert negative exponents into positive ones?
5. What is the simplified form of $\frac{a^{3/8}}{a^{1/4}}$?

Tip: When simplifying expressions involving exponents, always apply the exponent rules carefully, especially with fractional and negative exponents!