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.

A. 6^(-4)
B. (1/4)^(-3)
C. (1/2)^(-5)
D. 2^(-6)
E. 4(-3)

Answer 1

To find which expressions evaluate to \( \frac{1}{64} \), we can simplify each option.

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

B. \( (1/4)^{-3} \)
\[
(1/4)^{-3} = (4)^{3} = 64 \quad \text{(not } \frac{1}{64}\text{)}
\]

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

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

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

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

**D. \( 2^{-6} \)**
**E. \( 4^{-3} \)**

So the correct options are **D and E**.