To find which expressions evaluate to \( \frac{1}{64} \), let's evaluate each one:
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\( 6^{-4} \): \[ 6^{-4} = \frac{1}{6^4} = \frac{1}{1296} \quad (\text{not } \frac{1}{64}) \]
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\( \left( \frac{1}{4} \right)^{-3} \): \[ \left( \frac{1}{4} \right)^{-3} = \left( 4 \right)^{3} = 4^3 = 64 \quad (\text{not } \frac{1}{64}) \]
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\( 2^{-6} \): \[ 2^{-6} = \frac{1}{2^6} = \frac{1}{64} \quad (\text{is } \frac{1}{64}) \]
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\( 4^{-3} \): \[ 4^{-3} = \frac{1}{4^3} = \frac{1}{64} \quad (\text{is } \frac{1}{64}) \]
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\( \left( \frac{1}{2} \right)^{-5} \): \[ \left( \frac{1}{2} \right)^{-5} = \left( 2 \right)^{5} = 32 \quad (\text{not } \frac{1}{64}) \]
The correct expressions that evaluate to \( \frac{1}{64} \) are:
- \( 2^{-6} \)
- \( 4^{-3} \)
So the responses that apply are:
- \( 2^{-6} \)
- \( 4^{-3} \)