Let's fill in the blanks using the properties of exponents:
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From the equation \( 4^{2} = 16 = 64 ÷ _ \), we find that \( 64 ÷ 4 = 16 \), so the blank is 4.
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For \( 4^{0} = 4 ÷ 4 = _ \), we know that \( 4 ÷ 4 = 1 \), so the blank is 1.
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The equation \( 1/4 = 1/4^{(1)} \to 4^{(_)} = 1 ÷ 4 = 1/4 \) implies that \( 4^{-1} = 1/4 \). Therefore, the blank is -1.
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For \( 1/16 = 1/4^{(_)} \to 4^{(-2)} = 1/4 ÷ 4 = 1/_ \), we know that \( 1/16 = 1/4^{(2)} \), so \( 4^{-2} = 1/16 \). Therefore, the blank is 16.
Putting it all together:
- The first blank: 4
- The second blank: 1
- The third blank: -1
- The fourth blank: 16
Here's the completed table:
powers of 4
| 4^(3) = 64
| 4^(2) = 16 = 64 ÷ 4
| 4^(1) = 4 = 16 ÷ 4
| 4^(0) = 4 ÷ 4 = 1
| 1/4 = 1/4^(1) -> 4^(-1) = 1 ÷ 4 = 1/4
| 1/16 = 1/4^(2) -> 4^(-2) = 1/4 ÷ 4 = 1/16
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