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

2−6
2 to the negative 6 power

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

(12)−5
1 half to the negative 5 power

6−4
6 to the negative 4 power

4−3

Answer 1

To find which expressions could evaluate to \( \frac{1}{64} \), we need to evaluate each option:

1. **\( 2^{-6} \)**:
\[
2^{-6} = \frac{1}{2^6} = \frac{1}{64}
\]
This expression evaluates to \( \frac{1}{64} \).

2. **\( (14)^{-3} \)**:
\[
(14)^{-3} = \frac{1}{14^3}
\]
This does not evaluate to \( \frac{1}{64} \).

3. **\( (12)^{-5} \)**:
\[
(12)^{-5} = \frac{1}{12^5}
\]
This does not evaluate to \( \frac{1}{64} \).

4. **\( 6^{-4} \)**:
\[
6^{-4} = \frac{1}{6^4}
\]
This does not evaluate to \( \frac{1}{64} \).

5. **\( 4^{-3} \)**:
\[
4^{-3} = \frac{1}{4^3} = \frac{1}{64}
\]
This expression also evaluates to \( \frac{1}{64} \).

Thus, the expressions that could have been evaluated by Iris to give \( \frac{1}{64} \) are:

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

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