Question

Iris found a value of 1/64
when she evaluated an expression. Which could have been the expression Iris evaluated? Check the two that apply.(2 points)
Responses

(1/2)−5
1 half to the negative 5 power

6−4
6 to the negative 4 power

(1/4)−3
1 fourth to the negative 3 power

4−3
4 to the negative 3 power

2−6

Answer 1

To determine which expressions could evaluate to \( \frac{1}{64} \), we need to evaluate each expression one by one:

1. **\((1/2)^{-5}\)**
\[
(1/2)^{-5} = (2)^{5} = 32
\]
This does not equal \( \frac{1}{64} \).

2. **\(6^{-4}\)**
\[
6^{-4} = \frac{1}{6^4} = \frac{1}{1296}
\]
This does not equal \( \frac{1}{64} \).

3. **\((1/4)^{-3}\)**
\[
(1/4)^{-3} = (4)^{3} = 64
\]
This does not equal \( \frac{1}{64} \).

4. **\(4^{-3}\)**
\[
4^{-3} = \frac{1}{4^3} = \frac{1}{64}
\]
This equals \( \frac{1}{64} \).

5. **\(2^{-6}\)**
\[
2^{-6} = \frac{1}{2^6} = \frac{1}{64}
\]
This also equals \( \frac{1}{64} \).

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

- \(4^{-3}\)
- \(2^{-6}\)

So the correct options are:
- \(4^{-3}\)
- \(2^{-6}\)