Video: Multiplying Positive Rational (Unit Fraction) Expressions with Positive Integer Exponents

Which one of the following is equal to (1/3)³ × (1/3)²? [A] (1/3)⁵ [B] (1/3)⁶ [C] (1/9)⁶ [D] (1/9)⁵ [E] 1/54

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Video Transcript

Which one of the following is equal to one-third cubed multiplied by one-third squared? Is it A) one-third to the power of five, B) one-third to the power of six, C) one- ninth to the power of six, D) one-ninth to the power of five, or E) one fifty-fourth or one over 54?

As the fractions inside the brackets or parentheses are the same, we can use one of the laws of indices or exponents. 𝑥 to the power of 𝑎 multiplied by 𝑥 to the power of 𝑏 is equal to 𝑥 to the power of 𝑎 plus 𝑏. We can simply add the exponents or indices.

This means that one-third cubed multiplied by one-third squared is equal to one-third to the power of five as three plus two is equal to five. This means that the correct answer is option A. One-third to the power of five is equal to one-third cubed multiplied by one-third squared.

We could work out the actual value of this expression. One-third to the power of five is equal to one to the power of five divided by three to the power of five. One to the power of five is equal to one. And three to the power of five is equal to 243.

Therefore, one-third to the power of five is one over 243.

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