Let's fill in the blanks using the properties of exponents.
Powers of 4:
- \( 4^3 = 64 \)
- \( 4^2 = 16 = 64 \div 4 \) (So, the blank is 4)
- \( 4^1 = 4 = 16 \div 4 \)
- \( 4^0 = 4 \div 4 = 1 \) (So, the blank is 1)
- \( \frac{1}{4} = \frac{1}{4^1} \) -> \( 4^{-1} = 1 \div 4 = \frac{1}{4} \) (So, the blank is -1)
- \( \frac{1}{16} = \frac{1}{4^2} \) -> \( 4^{-2} = \frac{1}{4} \div 4 = \frac{1}{16} \) (So, the blank is 16)
Therefore, the completed table looks like this:
Powers of 4:
- \( 4^3 = 64 \)
- \( 4^2 = 16 = 64 \div 4 \)
- \( 4^1 = 4 = 16 \div 4 \)
- \( 4^0 = 4 \div 4 = 1 \)
- \( \frac{1}{4} = \frac{1}{4^1} -> 4^{-1} = 1 \div 4 = \frac{1}{4} \)
- \( \frac{1}{16} = \frac{1}{4^2} -> 4^{-2} = \frac{1}{4} \div 4 = \frac{1}{16} \)
Final Blanks Filled:
- \( 4 \) (from \( 16 \div 4 \))
- \( 1 \) (from \( 4 \div 4 \))
- \( -1 \) (from \( 4^{-1} \))
- \( 16 \) (as undefined based on \( 4^{-2} \) reverses \( \frac{1}{4^2} \))
These exponents indicate how powers of 4 diminish as the exponent decreases, and they also refer to negative powers indicating division.
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