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.