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?

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 $y = (4x + 3)^{\frac{3}{4}}$?

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