To evaluate \( 64^{-\frac{1}{3}} \):

1. First, recognize that the negative exponent means we take the reciprocal:
   \[
   64^{-\frac{1}{3}} = \frac{1}{64^{\frac{1}{3}}}
   \]

2. Next, find the cube root of 64:
   \[
   64^{\frac{1}{3}} = \sqrt[3]{64} = 4
   \]
   since \( 4^3 = 64 \).

3. Finally, take the reciprocal of 4:
   \[
   64^{-\frac{1}{3}} = \frac{1}{4}
   \]

Thus, \( 64^{-\frac{1}{3}} = \frac{1}{4} \).

Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:
1. What is \( 8^{-\frac{2}{3}} \)?
2. How do you evaluate \( 16^{-\frac{1}{4}} \)?
3. What is the cube root of \( 125 \)?
4. How do you simplify \( (64^{-1})^{\frac{1}{2}} \)?
5. What is the value of \( 100^{-\frac{1}{2}} \)?

**Tip**: When working with negative exponents, always remember to take the reciprocal of the base raised to the positive exponent!

Learn how to evaluate 64^(-1/3) by applying the laws of exponents and cube roots. This step-by-step solution breaks down exponentiation and shows how to take the reciprocal of a cube root, suitable for students in Grades 8-10.

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