Video: Dividing Positive Rational Expressions by Positive Integer Exponents

Which of the following has the same value as (1/3)³ ÷ (1/3)²? [A] 1/3 [B] (1/3)^(3/2) [C] (1/9)^(3/2) [D] 1/9 [E] 1^(3/2)

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Video Transcript

Which of the following has the same value as one-third cubed divided by one-third squared? Is it A) one-third, B) one-third to the power of three over two, C) one-ninth to the power of three over two, D) one-ninth, or E) one to the power of three over two.

As the fractions inside the brackets or parentheses are the same, we can use one of the laws of indices or exponents. 𝑎 to the power of 𝑥 divided by 𝑎 to the power of 𝑦 is equal to 𝑎 to the power of 𝑥 minus 𝑦. We can subtract the exponents or indices. This means that one-third cubed divided by one-third squared is equal to one-third to the power of one as three minus two is equal to one.

Any number raised to the power of one is equal to itself. This means that one-third to the power of one is equal to one-third. This means that the correct answer is A.

One-third has the same value as one-third cubed divided by one-third squared.

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