https://r2.erweima.ai/mathbot/image/1726032707663hqdiys2g.jpg

The equation in the image is:

\[
S = \sqrt[3]{ \sqrt[3]{ \frac{2}{x^4} } \cdot \sqrt[3]{ \frac{3}{x^5} } } \cdot \sqrt[3]{ \sqrt[4]{ \frac{4}{x^5} } }
\]

We are asked to simplify and reduce this expression.

### Step-by-Step Solution:
#### 1. Simplify the nested cube roots:
The expression consists of several cube roots and fourth roots of fractions. Begin by simplifying the inner terms.

#### 2. Combine like terms:
For cube and fourth roots of powers of \( x \), use the properties of exponents:
\[
\sqrt[n]{\frac{a}{x^m}} = \frac{a^{1/n}}{x^{m/n}}
\]

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If you'd like, I can guide you through the manual steps to simplify the given expression, or we can try again later. Let me know how you'd like to proceed!

Simplify and reduce the expression S = (cube root of (cube root of (2/x^4) times cube root of (3/x^5))) times cube root of (fourth root of (4/x^5)).

Explore the process of simplifying complex expressions involving nested cube and fourth roots with fractional exponents. This detailed guide provides a step-by-step approach to handling fractional powers and combining like terms in algebraic expressions.

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