To determine which expressions could equal 164, we will evaluate each of the mathematical expressions given:
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(12)−5 or \( \left( \frac{1}{2} \right)^{-5} \): \[ \left( \frac{1}{2} \right)^{-5} = 2^5 = 32 \quad (\text{Not 164}) \]
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6−4 or \( 6^{-4} \): \[ 6^{-4} = \frac{1}{6^4} = \frac{1}{1296} \quad (\text{Not 164}) \]
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(14)−3 or \( \left( \frac{1}{4} \right)^{-3} \): \[ \left( \frac{1}{4} \right)^{-3} = 4^3 = 64 \quad (\text{Not 164}) \]
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4−3 or \( 4^{-3} \): \[ 4^{-3} = \frac{1}{4^3} = \frac{1}{64} \quad (\text{Not 164}) \]
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2−6 or \( 2^{-6} \): \[ 2^{-6} = \frac{1}{2^6} = \frac{1}{64} \quad (\text{Not 164}) \]
None of the given expressions produce a result of 164 based on the evaluations provided. Thus, there are no expressions from the list that could have resulted in 164.
If there were additional options available outside the given list or if there was more context around the original expression that led to 164, please share that information for further assistance.
1 answer