the square root goes over the x(squared) -1 and is to the power of ^3

You are describing the mathematical expression:

\[
\left(\sqrt{x^2 - 1}\right)^3
\]

This expression can be interpreted as:

1. **Inside the square root**: First, calculate \(x^2 - 1\).
2. **Square root**: Then, take the square root of the result.
3. **Cubing**: Finally, raise the square root to the power of 3.

So, the expression simplifies to:

\[
\left(\sqrt{x^2 - 1}\right)^3
\]

Would you like to explore further details, such as solving for specific values of \(x\) or analyzing the behavior of this function? 

Here are 5 related questions:
1. What is the domain of \(\sqrt{x^2 - 1}\)?
2. How does the expression change if you simplify \(\left(\sqrt{x^2 - 1}\right)^3\)?
3. What is the derivative of this expression with respect to \(x\)?
4. What happens when you substitute specific values of \(x\) into this expression?
5. How would this expression be graphed on a coordinate plane?

**Tip:** When dealing with complex expressions, always simplify the inner expressions first before applying the outer operations.

Explore the mathematical expression (sqrt(x^2 - 1))^3 with detailed explanations and examples. Learn how to interpret and simplify this expression step-by-step. Suitable for high school students and anyone interested in advanced algebraic concepts.

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