Let's break down the problem step by step:

### Step 1: Evaluate \( g(\sqrt[3]{216}) \)
The cube root of 216 is:

\[
\sqrt[3]{216} = 6
\]

Thus, the problem becomes:

\[
g(6) = |x^3 - 29|
\]

### Step 2: Substitute \( g(6) \) into the function
Now, we substitute 6 into the right-hand side, where \( x = 6 \):

\[
|6^3 - 29| = |216 - 29|
\]

### Step 3: Simplify
Now, simplify the expression inside the absolute value:

\[
216 - 29 = 187
\]

Thus:

\[
|187| = 187
\]

### Final Answer:
\[
g(6) = 187
\]

Would you like more details or have any questions?

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Here are 5 related questions you might want to explore:
1. How do cube roots relate to exponents and logarithms?
2. What is the general rule for solving absolute value equations?
3. How can you visualize cube roots on a number line?
4. How does the function \( g(x) = |x^3 - 29| \) behave for different values of \( x \)?
5. What are some real-world applications of cube roots?

**Tip:** Always simplify any roots or exponents before applying functions like absolute value to avoid calculation errors!

Explore how to solve g(³√216)=|x³-29| with a step-by-step breakdown. This solution covers cube roots, absolute value, and basic algebra concepts. Ideal for students in Grades 8-10 looking to strengthen their understanding of algebraic functions.

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