The expression shown in the image is:

$\sqrt[9]{(x + 4)^6}$

This represents the ninth root of $(x + 4)^6$. To simplify this, we can apply the properties of exponents and radicals.

The general rule for roots and exponents is:

$\sqrt[n]{a^m} = a^{\frac{m}{n}}$

So, applying this to your expression:

$\sqrt[9]{(x + 4)^6} = (x + 4)^{\frac{6}{9}} = (x + 4)^{\frac{2}{3}}$

Thus, the simplified form of the expression is:

$(x + 4)^{\frac{2}{3}}$

Would you like more details on this or further explanations?

Here are 5 related questions to deepen your understanding:

1. What is the general rule for simplifying expressions involving radicals and exponents?
2. How would you simplify $\sqrt[4]{(x + 3)^8}$?
3. Can you express $(x + 4)^{\frac{2}{3}}$ in radical form?
4. What happens if the exponent in the denominator is negative in such expressions?
5. How do you differentiate $(x + 4)^{\frac{2}{3}}$ with respect to $x$?

Tip: Always remember that taking roots can be seen as applying fractional exponents. A square root is the same as raising to the power of $\frac{1}{2}$, and similarly for other roots.