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The expression given is \( 4^{-3} \).

To simplify this:

1. The negative exponent rule states that \( a^{-b} = \frac{1}{a^b} \), so:
   \[
   4^{-3} = \frac{1}{4^3}
   \]
   
2. Now, calculate \( 4^3 \):
   \[
   4^3 = 4 \times 4 \times 4 = 64
   \]

Thus, the equivalent expression is:
\[
4^{-3} = \frac{1}{64}
\]

Would you like further details on the process or have any questions?

Here are 5 related questions to expand on this:
1. How do you simplify expressions with negative exponents in general?
2. Can you explain how to simplify \( a^{-n} \times a^n \)?
3. How would you handle an expression like \( (2^3)^{-2} \)?
4. What happens when the base of the exponent is a fraction, such as \( \left(\frac{1}{2}\right)^{-3} \)?
5. How can negative exponents be used to represent very small numbers?

**Tip**: Whenever you encounter a negative exponent, remember that it flips the base into its reciprocal, making it a fraction.

Select the equivalent expression for 4^(-3)

Learn how to simplify the expression 4^(-3) using the negative exponent rule. This detailed explanation covers how negative exponents flip the base into its reciprocal, making the answer 1/64. Suitable for students in Grades 7-9.

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