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Which of the following has the same value as two-thirds to the negative third power divided by two-thirds to the negative fourth power?
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A) two-thirds, B) one, C) two-thirds to the three-fourths power, D) three-halves to the negative seventh power, or E) two-thirds to the negative seventh power.
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Here we can see that we are dividing with like bases of two-thirds.
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And we can use the property that 𝑥 to the 𝑎 power divided by 𝑥 to the 𝑏 power is equal to 𝑥 to the 𝑎 minus 𝑏 power.
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So we have two-thirds to the negative third power divided by two-thirds to the negative fourth power, which would be equal to two-thirds to the negative three minus negative four power.
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And two negatives make a positive.
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So negative three plus four is equal to one.
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And two-thirds to the one power would be two to the first power divided by three of the first power, which is equal to two-thirds.
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So our final answer is two-thirds.
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So we would need to choose option A.