Question

Fill in the blanks!
Use the powers of 4 in the table to evaluate power that have zero and _ exponents.

powers of 4
|
4^(3) = 64
4^(2) = 16 = 64 ÷ _
4^(1) = 4 = 16 ÷ 4
4^(0) = 4 ÷ 4 = _
1/4 = 1/4^(1) -> 4^(_) = 1 ÷ 4 = 1/4
1/16 = 1/4^(_) -> 4^(-2) = 1/4 ÷ 4 = 1/_

Answer 1

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:
1. \( 4 \) (from \( 16 \div 4 \))
2. \( 1 \) (from \( 4 \div 4 \))
3. \( -1 \) (from \( 4^{-1} \))
4. \( 16 \) (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.