The problem in the image asks for the simplified form of the expression:

$\frac{\sqrt[3]{a^2 \sqrt{a}}}{a}$

Let's break it down step by step to simplify the expression.

Step 1: Simplify the expression inside the cube root.

The term inside the cube root is $a^2 \sqrt{a}$. We know that $\sqrt{a}$ is the same as $a^{1/2}$. So, we can rewrite the expression as:

$a^2 \cdot a^{1/2} = a^{2 + 1/2} = a^{5/2}$

Step 2: Apply the cube root.

Now we apply the cube root to $a^{5/2}$. The cube root of a power of $a$ is the same as raising the exponent to $1/3$:

$\sqrt[3]{a^{5/2}} = a^{(5/2) \cdot (1/3)} = a^{5/6}$

Step 3: Simplify the entire expression.

Now we have:

$\frac{a^{5/6}}{a} = a^{5/6 - 1} = a^{5/6 - 6/6} = a^{-1/6}$

Step 4: Express the result.

The simplified form of the given expression is $a^{-1/6}$.

This matches option (b) in the image.

Would you like a further breakdown of any of these steps?

Related questions:

1. How do you simplify expressions involving roots and exponents?
2. What are the rules for simplifying fractional exponents?
3. How do you handle cube roots in algebraic expressions?
4. Can you explain how to apply exponent subtraction in more detail?
5. What is the difference between cube roots and square roots in algebraic expressions?

Tip: When simplifying expressions with both square and cube roots, it's often helpful to convert everything into fractional exponents first.