https://file.aiquickdraw.com/mathbot/file/1726367097577avv0bezm.jpg

The equation shown in the image is:

\[
\left( \frac{1}{4} \right)^{-3}
\]

To solve this:

1. **Apply the negative exponent rule**: When a fraction is raised to a negative exponent, we can flip the fraction and change the sign of the exponent. So:

\[
\left( \frac{1}{4} \right)^{-3} = \left( \frac{4}{1} \right)^3
\]

2. **Simplify**: Now, raise 4 to the power of 3:

\[
4^3 = 4 \times 4 \times 4 = 64
\]

Therefore:

\[
\left( \frac{1}{4} \right)^{-3} = 64
\]

So, the answer to the blank in the image should be **64**.

Would you like a more detailed breakdown, or do you have any further questions?

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Here are 5 questions for further practice:

1. What is \(\left( \frac{1}{3} \right)^{-2}\)?
2. How do you simplify \(\left( \frac{2}{5} \right)^{-3}\)?
3. What is the result of \(\left( \frac{5}{6} \right)^{-2}\)?
4. Can you explain the general rule for dealing with negative exponents?
5. How do you compute \(\left( \frac{1}{2} \right)^{-4}\)?

**Tip**: When you have a negative exponent, just flip the fraction to make the exponent positive!

Learn how to simplify the negative exponent expression (1/4)^(-3) by applying the negative exponent rule and understanding fraction powers. This problem is suitable for students in grades 6-8, covering key concepts like exponents and fractions.

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