Question

Iris found a value of 1
64
when she evaluated an expression.

Which could have been the expression Iris evaluated? Check all that apply.
2-6
6-4
4-3
(one-half) Superscript negative 5
(one-fourth) Superscript negative 3

Answer 1

To determine which expressions could evaluate to \( \frac{1}{64} \), let's evaluate each option:

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

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

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

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

5. **\( \left( \frac{1}{4} \right)^{-3} \)**
\[
\left( \frac{1}{4} \right)^{-3} = 4^3 = 64 \quad \text{(you can also write this as } \frac{1}{4^{-3}} = \frac{1}{\left( \frac{1}{4} \right)^{-3}} = \frac{1}{\frac{1}{64}} = 64 \text{ which is the same)}
\]
This is equal to \( 64\) but we need \( \frac{1}{64} \), so it does not equal \( \frac{1}{64} \).

From the analysis above, none of the expressions evaluate to \( \frac{1}{64} \).

Therefore, **none** of the options provided could have been the expression Iris evaluated.