The image you uploaded seems to contain an expression with multiple nested radicals. Let me break down the expression for you and solve it step by step.

The expression appears as follows: [ \sqrt[3]{\sqrt{32^{4/4}}} \cdot \sqrt{\sqrt{2^{4}} \cdot \sqrt[3]{4^{3/4}}} ]

I will solve it in parts. Here's how:

Step 1: Simplify $\sqrt[3]{\sqrt{32^{4/4}}}$

1. Simplify $32^{4/4}$, which equals $32$.
2. Now, calculate $\sqrt{32}$.
3. Then, apply the cube root to the result.

Step 2: Simplify $\sqrt{\sqrt{2^{4}} \cdot \sqrt[3]{4^{3/4}}}$

1. Simplify $2^{4} = 16$, so $\sqrt{2^{4}} = \sqrt{16} = 4$.
2. Simplify $4^{3/4}$. Since $4 = 2^2$, then $4^{3/4} = (2^2)^{3/4} = 2^{3/2} = \sqrt{8}$.
3. Now, calculate $\sqrt{4 \cdot \sqrt{8}}$.

I'll go ahead and perform the calculations. sympy as sp

Define the expressions

expr1 = sp.cbrt(sp.sqrt(32**(4/4))) expr2 = sp.sqrt(sp.sqrt(24) * sp.cbrt(4(3/4)))

Calculate the result

result = expr1 * expr2 result.evalf()The result of the expression is approximately $4.24$.

Would you like a more detailed breakdown of the steps, or do you have any other questions on this? Here are some related questions you could explore:

1. How do you simplify nested radicals step by step?
2. What are the properties of cube roots and square roots when combined in an expression?
3. How do fractional exponents affect the simplification of an expression?
4. Can you simplify more complex expressions involving both roots and exponents?
5. What is the difference between simplifying expressions with even and odd roots?

Tip: When dealing with nested radicals, it's helpful to simplify the inner expressions first before dealing with the outer operations.