Let's analyze the problem visible in your uploaded image. The question asks to simplify the expression:

$\sqrt[3]{27u^9}.$

Steps to Simplify:

1. Simplify the cube root of the constant term:
   $\sqrt[3]{27} = 3.$

2. Simplify the cube root of the variable term:
   Using the property of exponents $(a^m)^n = a^{m \cdot n}$, we have: $\sqrt[3]{u^9} = u^{9/3} = u^3.$

3. Combine the results:
   Multiplying the simplified terms gives: $\sqrt[3]{27u^9} = 3u^3.$

Final Answer:

$3u^3.$

It seems your answer might not match this, so ensure you use this approach.

Would you like further clarification or an alternative explanation? Here are some follow-up questions:

1. What are the key differences between simplifying square roots and cube roots?
2. How do you handle fractional exponents for cube roots?
3. Why do we treat constants (like 27) separately from variables when simplifying?
4. Could we apply similar steps to $\sqrt[3]{64x^{12}}$?
5. What properties of exponents are useful for simplifying cube roots?

Tip:

Always rewrite roots as fractional exponents, as it makes simplification more straightforward!