Math Problem Statement

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

Solution

The table asks to fill in values for 4x4^x where xx takes on values from −2-2 to 22. Let's compute each of these powers:

  1. 4−2=142=1164^{-2} = \frac{1}{4^2} = \frac{1}{16}
  2. 4−1=141=144^{-1} = \frac{1}{4^1} = \frac{1}{4}
  3. 40=14^0 = 1 (anything raised to the power of 0 is 1)
  4. 41=44^1 = 4
  5. 42=164^2 = 16

So, the completed table should be:

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.

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Math Problem Analysis

Mathematical Concepts

Exponentiation
Negative Exponents

Formulas

4^x
4^{-n} = 1 / 4^n

Theorems

Any number raised to the power of 0 is 1
Negative exponents represent the reciprocal of the positive exponent

Suitable Grade Level

Grades 6-8

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