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

Which of the following is equal to (−2)⁵ × (−2)⁻³? [A] (−2)⁻¹⁵ [B] 1/4 [C] 4 [D] −4 [E] 4²

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Video Transcript

Which of the following is equal to negative two to the power of five multiplied by negative two to the power of negative three? Is it (A) negative two to the power of negative 15, (B) one-quarter, (C) four, (D) negative four, or (E) four squared?

In order to answer this question, we need to 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 the base is the same, when multiplying, we can add the exponents or indices.

In this case, negative two to the power of five multiplied by negative two to the power of negative three is equal to negative two to the power of five plus negative three. This is the same as negative two to the power of five minus three, which in turn simplifies to negative two to the power of two or negative two squared.

Squaring a number means multiplying it by itself. In this case, we need to multiply negative two by negative two. Multiplying a negative number by a negative number gives a positive answer. Therefore, negative two squared is four. The correct answer is option (C). Negative two to the power of five multiplied by negative two to the power of negative three is equal to four.

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