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)

1 answer

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.