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Let's break down the expression and solve it step by step:

You are given the expression:

\[
\left( 64^{1/3} \right)^{-1}
\]

### Step 1: Simplify \( 64^{1/3} \)

\( 64^{1/3} \) means the cube root of 64. Since \( 64 = 4^3 \), we have:

\[
64^{1/3} = 4
\]

### Step 2: Apply the negative exponent

Now, we need to evaluate \( 4^{-1} \). Recall that a negative exponent means taking the reciprocal, so:

\[
4^{-1} = \frac{1}{4}
\]

### Final Answer:
The simplified and evaluated result is:

\[
\boxed{\frac{1}{4}}
\]

Would you like further clarification on any steps or additional details?

### Related Questions:
1. What is the general rule for simplifying fractional exponents?
2. How do you handle negative exponents in other cases, such as \( a^{-n} \)?
3. Can you explain how \( (a^m)^n \) works when both exponents are fractional?
4. How would you approach \( (x^a)^b \) for any real number \( x \) and exponents \( a, b \)?
5. What happens when the base of the exponent is negative and has a fractional exponent?

### Tip:
When dealing with fractional exponents, remember that \( a^{m/n} \) means the \( n \)-th root of \( a \) raised to the \( m \)-th power!

Simplify and then evaluate (64^(1/3))^(-1) (Give your answer as a fraction.)

Solve the expression (64^(1/3))^(-1) with detailed steps. Learn about cube roots and negative exponents. This problem is perfect for students in Grades 9-10 studying algebraic exponents.

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