Video: Evaluating Positive Rational Expressions with Negative Integer Exponents Raised to Negative Integer Exponents

Which of the following has the same value as ((1/2)⁻³)⁻⁴? [A] −(1/2)¹² [B] (1/2)⁻¹² [C] (1/2)⁻⁷ [D] (1/2)¹² [E] 2

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Video Transcript

Which of the following has the same value as one-half to the power of negative three all to the power of negative four? Is it (A) negative one-half to the power of 12, (B) one-half to the power of negative 12, (C) one-half to the power of negative seven, (D) one-half to the power of 12, or (E) two?

In order to answer this question, we need to recall one of our laws of exponents or indices. 𝑥 to the power of 𝑎 all to the power of 𝑏 is equal to 𝑥 to the power of 𝑎𝑏. When a value raised to a power is raised to another power, we need to multiply the two exponents. In this case, we need to multiply negative three and negative four. Multiplying two negative numbers gives a positive answer. Therefore, our expression simplifies to one-half to the power of 12.

The correct answer is option (D). A half to the power of negative three all to the power of negative four is equal to a half to the power of 12.

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