Video: Multiplying Positive Integer Expressions with Mixed Positive and Negative Integer Exponents

Which of the following is equal to 3⁻² × 3⁵? [A] 3³ [B] 3⁻³ [C] 3⁻¹⁰ [D] 9³ [E] −90

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Video Transcript

Which of the following is equal to three to the power of negative two multiplied by three to the power of five. Is it (A) three cubed, (B) three to the power of negative three, (C) three to the power of negative 10, (D) nine to the power of three, or (E) negative 90?

In order to answer this question, we recall one of our laws of exponents or indices. 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. As long as our base numbers are the same, when multiplying, we can add the exponents.

This means that three to the power of negative two multiplied by three to the power of five is equal to three to the power of negative two plus five. As negative two plus five is equal to three, this simplifies to three to the power of three or three cubed. Three to the power of negative two multiplied by three to the power of five is equal to three cubed. The correct answer is option (A).

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