To express $(7x + 3)^{\frac{3}{4}}$ in radical notation, recall that an exponent of $\frac{m}{n}$ can be rewritten as the $n$-th root of the base raised to the $m$-th power. Thus, $(a^{\frac{m}{n}} = \sqrt[n]{a^m})$.

Given this:

$(7x + 3)^{\frac{3}{4}} = \sqrt[4]{(7x + 3)^3}$

This is already in its simplified form. So, the expression in radical notation is:

$\sqrt[4]{(7x + 3)^3}$

Let me know if you need more details on this explanation!

Related Questions:

1. How would the expression change if the exponent was $\frac{5}{6}$?
2. Can you explain how to handle fractional exponents in a general way?
3. What happens to the expression if $x = 1$?
4. How would you simplify $\sqrt[4]{(7x + 3)^2}$?
5. What does the cube root of a variable represent geometrically?

Tip: For fractional exponents, the numerator represents a power and the denominator represents a root.