Question

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

Answer 1

fill in the blank please

Answer 2

To evaluate powers of 4 with zero and negative exponents, we can use the following properties of exponents:

1. Any non-zero number raised to the power of zero equals 1:
\[
4^0 = 1
\]

2. A negative exponent represents the reciprocal of the base raised to the positive exponent:
\[
4^{-n} = \frac{1}{4^n}
\]

Based on these rules, we find the values for powers of 4 with zero and negative exponents:

- For zero exponent:
\[
4^0 = 1
\]

- For negative exponents:
- \( 4^{-1} = \frac{1}{4} \)
- \( 4^{-2} = \frac{1}{4^2} = \frac{1}{16} \)
- \( 4^{-3} = \frac{1}{4^3} = \frac{1}{64} \)
- \( 4^{-4} = \frac{1}{4^4} = \frac{1}{256} \)

So, you can fill in the blanks as follows:

- **Zero exponent**: \( 4^0 = 1 \)
- **Negative exponents**:
- \( 4^{-1} = \frac{1}{4} \)
- \( 4^{-2} = \frac{1}{16} \)
- \( 4^{-3} = \frac{1}{64} \)
- \( 4^{-4} = \frac{1}{256} \)

Let me know if you need more calculations or a different range!

Answer 3

Sure! Here’s a simple table that shows the powers of 4, specifically for zero and negative exponents. I’ll provide the answers for the blanks.

| Exponent | Value |
|----------|--------------------------------|
| \(4^0\) | **1** |
| \(4^{-1}\)| **\(\frac{1}{4}\)** |
| \(4^{-2}\)| **\(\frac{1}{16}\)** |
| \(4^{-3}\)| **\(\frac{1}{64}\)** |
| \(4^{-4}\)| **\(\frac{1}{256}\)** |

So, filling in the blanks:

- \(4^0 = 1\)
- \(4^{-1} = \frac{1}{4}\)
- \(4^{-2} = \frac{1}{16}\)
- \(4^{-3} = \frac{1}{64}\)
- \(4^{-4} = \frac{1}{256}\)

Let me know if you need anything else!