Use radical notation to write the expression. Simplify if possible. Assume that all variables represent positive real numbers.
(7x+3)^3/4=

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.

Use radical notation to write the expression. Simplify if possible. Assume that all variables represent positive real numbers. (7x+3)^3/4=

Learn how to simplify the expression (7x+3)^(3/4) by converting it to radical notation. This solution explains key concepts like fractional exponents, the radical theorem, and the laws of exponents. Ideal for students in Grades 10-12.

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