To simplify $\sqrt[3]{x^{27}}$, let's break it down step-by-step.

1. Start with the expression:

   $\sqrt[3]{x^{27}}$

2. Recall that the cube root of a number is the same as raising that number to the power of $\frac{1}{3}$. So, we can rewrite the cube root as:

   $(x^{27})^{\frac{1}{3}}$

3. Apply the power rule $(a^m)^n = a^{m \cdot n}$. This gives:

   $x^{27 \cdot \frac{1}{3}} = x^9$

So, the simplified expression is:

$x^9$

Final Answer:

$\sqrt[3]{x^{27}} = x^9$

Would you like further details on any step?

Here are 5 related questions:

1. How do you simplify a cube root for variables with different exponents?
2. What is the power rule for exponents?
3. How do you simplify higher roots, such as fourth or fifth roots?
4. What are some practical applications of cube roots in real-world problems?
5. How do you simplify expressions with multiple variables under cube roots?

Tip: When dealing with exponents and roots, always remember that $\sqrt[n]{x^m} = x^{\frac{m}{n}}$.