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.
A. 2-6
B. 6-4
C. 4-3
D. (one-half) Superscript negative 5
E. (one-fourth) Superscript negative 3

Answer 1

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

A. \( 2 - 6 = -4 \)
Does not equal \( \frac{1}{64} \).

B. \( 6 - 4 = 2 \)
Does not equal \( \frac{1}{64} \).

C. \( 4 - 3 = 1 \)
Does not equal \( \frac{1}{64} \).

D. \( \left(\frac{1}{2}\right)^{-5} = 2^5 = 32 \)
Does not equal \( \frac{1}{64} \).

E. \( \left(\frac{1}{4}\right)^{-3} = 4^3 = 64 \)
The reciprocal of \( 64 \) is \( \frac{1}{64} \).

Thus, the only expression that evaluates to \( \frac{1}{64} \) is:

**E. \( \left(\frac{1}{4}\right)^{-3} \)**.

So, the answer is **E**.