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The uploaded image shows the expression \((4x + 3)^{\frac{3}{4}}\). This expression involves a power with a fractional exponent. Let's break it down and offer insights into how to work with it.

### Key Details:
- The **base** is \(4x + 3\).
- The **exponent** is \(\frac{3}{4}\), which has the following meaning:
  - The **denominator (4)** represents a fourth root.
  - The **numerator (3)** indicates raising the result to the power of 3.

### Simplification / How to Handle:
1. **Rewrite the fractional exponent**:  
   \[
   (4x + 3)^{\frac{3}{4}} = \left(\sqrt[4]{4x + 3}\right)^3
   \]
   Alternatively, it can also be expressed as:
   \[
   (4x + 3)^{\frac{3}{4}} = \sqrt[4]{(4x + 3)^3}
   \]
2. **Evaluating or simplifying**:  
   This depends on whether you're working with specific values of \(x\). If \(x\) is known, you can substitute it and compute the expression directly. However, if left general, it typically stays in the simplified radical-exponent form shown above.

Would you like a more detailed expansion, such as:
- Handling this expression in calculus (e.g., differentiation or integration)?
- Graphing behavior of this function?

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### Related Questions:
1. What happens when you differentiate \((4x + 3)^{\frac{3}{4}}\) with respect to \(x\)?
2. How do you solve an equation involving \((4x + 3)^{\frac{3}{4}} = 8\)?
3. Can fractional exponents be negative? How does it affect the calculation?
4. What is the difference between \(\sqrt[4]{4x + 3}\) and \((4x + 3)^{\frac{1}{4}}\)?
5. How would you graph the function \(y = (4x + 3)^{\frac{3}{4}}\)?

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**Tip**: Fractional exponents are useful because they unify the concepts of roots and powers.

Learn how to simplify the algebraic expression (4x + 3)^{3/4} using fractional exponents and radicals. This step-by-step solution covers key concepts from algebra, including powers, roots, and exponents. Suitable for high school students in Grades 10-12.

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