Math Problem Statement

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

Solution

It looks like the mathematical expression in the image is:

(2x34x5)3\left(\frac{2x^3}{4x-5}\right)^3

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

2x34x5=2x34x5\frac{2x^3}{4x-5} = \frac{2x^3}{4x-5}

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

(2x34x5)3=(2x3)3(4x5)3=8x9(4x5)3\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:

8x9(4x5)3\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=0x = 0?
  2. How would the expression change if x=1x = 1?
  3. What are the implications if x=54x = \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.

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Math Problem Analysis

Mathematical Concepts

Algebra
Exponentiation
Fractions

Formulas

Simplifying fractions
Exponentiation of fractions (a/b)^n = (a^n)/(b^n)

Theorems

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Suitable Grade Level

Grades 10-12