https://file.aiquickdraw.com/mathbot/file/1726955625280v725p7yd.jpg

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.

Simplify the expression \(\sqrt[9]{(x + 4)^6}\).

Learn how to simplify the expression \(\sqrt[9]{(x + 4)^6}\) by applying the properties of exponents and radicals. This algebra problem involves simplifying radicals and fractional exponents, making it suitable for students in Grades 10-12.

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