Fill in the blanks!

Question

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

Answer 1

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 2

fill in the blank please

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!