Video: Dividing Positive Rational Expressions by Negative Integer Exponents

Which of the following has the same value as (2/3)⁻³ ÷ (2/3)⁻⁴? [A] 2/3 [B] 1 [C] (2/3)³ᐟ⁴ [D] (3/2)⁻⁷ [E] (2/3)⁻⁷.

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Video Transcript

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? 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.

Here we can see that we are dividing with like bases of two-thirds. 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.

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. And two negatives make a positive. So negative three plus four is equal to one. 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. So our final answer is two-thirds. So we would need to choose option A.

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