https://file.aiquickdraw.com/mathbot/file/17270495467124fha5i51.jpg

It looks like the mathematical expression in the image is:

\[
\left(\frac{2x^3}{4x-5}\right)^3
\]

To solve or simplify this expression, you first simplify the fraction inside the parenthesis:

\[
\frac{2x^3}{4x-5} = \frac{2x^3}{4x-5}
\]

Since the expression itself doesn't simplify any further without specific values for \(x\), the next step is to calculate the cube:

\[
\left(\frac{2x^3}{4x-5}\right)^3 = \frac{(2x^3)^3}{(4x-5)^3} = \frac{8x^9}{(4x-5)^3}
\]

The final simplified form of the expression is:

\[
\frac{8x^9}{(4x-5)^3}
\]

Would you like to explore this expression further or do you have any questions about the steps taken? Here are a few follow-up questions:

1. What happens to the expression when \( x = 0 \)?
2. How would the expression change if \( x = 1 \)?
3. What are the implications if \( x = \frac{5}{4} \), where the denominator becomes zero?
4. How can we find the derivative of this expression?
5. How does the graph of this function look like?

**Tip:** When working with expressions raised to a power, always consider simplifying the base before applying the exponent to make calculations easier.

Simplify and calculate the expression (2x^3 / (4x - 5))^3.

Learn how to simplify and calculate the expression (2x^3 / (4x - 5))^3 by breaking down the fraction and applying exponentiation. This detailed solution is suitable for students in Grades 10-12 covering key algebraic concepts.

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