Question Video: Applying the Law of Negative Exponents

Which of the following is equal to 46^(-1)? [A] 1/46 [B] 46 [C] 45 [D] 1/45 [E] 0.46

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Video Transcript

Which of the following is equal to 46 to the power of negative one? (A) One over 46, (B) 46, (C) 45, (D) one over 45, or (E) 0.46.

Well, what we can recall is that we’ve got 𝑥 to the power of negative 𝑛 equals one over 𝑥 to the power of 𝑛. So, this is one of the rules that we have of our exponents. So, from this, we can see that 𝑥 to the power of negative one is gonna be equal to one over 𝑥. So therefore, this, in fact, is gonna be the reciprocal. So, let’s take a look at what we’ve got. We’ve got 46 to the power of negative one. Well, if we think of 46 as 46 over one, then 46 to the power of negative one is gonna be the reciprocal of 46 over one. Which is gonna give us one over 46 because what we do is we flip the numerator and the denominator to find our reciprocal.

So therefore, we can say that answer (A) is equal to 46 to the power of negative one. And that’s because answer (A) is one over 46.

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