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The table asks to fill in values for \( 4^x \) where \( x \) takes on values from \( -2 \) to \( 2 \). Let's compute each of these powers:

1. \( 4^{-2} = \frac{1}{4^2} = \frac{1}{16} \)
2. \( 4^{-1} = \frac{1}{4^1} = \frac{1}{4} \)
3. \( 4^0 = 1 \) (anything raised to the power of 0 is 1)
4. \( 4^1 = 4 \)
5. \( 4^2 = 16 \)

So, the completed table should be:

\[
\begin{array}{c|c}
x & 4^x \\
\hline
-2 & \frac{1}{16} \\
-1 & \frac{1}{4} \\
0  & 1 \\
1  & 4 \\
2  & 16 \\
\end{array}
\]

Would you like more details or have any questions about how these values were calculated?

Here are five related questions:
1. What is \( 4^3 \)?
2. How do negative exponents affect the value of a number?
3. What is the general formula for calculating powers with negative exponents?
4. What happens when the base is 1 and you apply different exponents to it?
5. How would the table change if the base were 3 instead of 4?

**Tip**: Remember that any number raised to the power of 0 is always 1, regardless of the base.

Fill in the table for powers of 4 with x values ranging from -2 to 2.

Learn how to calculate powers of 4 for exponents ranging from -2 to 2. This problem demonstrates the rules of exponentiation, including negative exponents, and provides a step-by-step solution suitable for Grades 6-8.

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