Iris found a value of 1over64

Question

when she evaluated an expression. Which could have been the expression Iris evaluated? Check the two that apply.(2 points)
Responses

6−4
6 to the negative 4 power

(14)−3
1 fourth to the negative 3 power

2−6
2 to the negative 6 power

4−3
4 to the negative 3 power

(12)−5

Answer 1

To find which expressions evaluate to \( \frac{1}{64} \), let's evaluate each one:

1. \( 6^{-4} \): \[ 6^{-4} = \frac{1}{6^4} = \frac{1}{1296} \quad (\text{not } \frac{1}{64}) \]

2. \( \left( \frac{1}{4} \right)^{-3} \): \[ \left( \frac{1}{4} \right)^{-3} = \left( 4 \right)^{3} = 4^3 = 64 \quad (\text{not } \frac{1}{64}) \]

3. \( 2^{-6} \): \[ 2^{-6} = \frac{1}{2^6} = \frac{1}{64} \quad (\text{is } \frac{1}{64}) \]

4. \( 4^{-3} \): \[ 4^{-3} = \frac{1}{4^3} = \frac{1}{64} \quad (\text{is } \frac{1}{64}) \]

5. \( \left( \frac{1}{2} \right)^{-5} \): \[ \left( \frac{1}{2} \right)^{-5} = \left( 2 \right)^{5} = 32 \quad (\text{not } \frac{1}{64}) \]

The correct expressions that evaluate to \( \frac{1}{64} \) are:

• \( 2^{-6} \)
• \( 4^{-3} \)

So the responses that apply are:

• \( 2^{-6} \)
• \( 4^{-3} \)