Question Video: Evaluating Numerical Expressions Involving Negative Powers

Calculate (2⁻² ⋅ 3⁻¹)⁻¹, giving your answer in its simplest form.

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Video Transcript

Calculate two to the power of negative two multiplied by three to the power of negative one all to the power of negative one, giving your answer in its simplest form.

So, first of all, what we’re doing is we’re gonna use our rule that we have — that’s 𝑥 to the power of negative 𝑛 equals one over 𝑥 to the power of 𝑛 — to convert our negative exponents into factions. So, first of all, we’re gonna have two to the power of negative two. And this’s gonna be equal to one over two squared, which is gonna be equal to one over four. So, we can say that two to the power of negative two is equal to a quarter. Then, next, what we have is three to the power of negative one. And we know that three to the negative one is gonna be equal to one over three. And that’s because it’s the reciprocal of three over one. So, three over one is what three is. Reciprocal of that is one over three. Okay, great, we’ve converted them both into fractions.

Okay, great, so, now, what we have is a quarter multiplied by a third all to the power of negative one. Well, if we multiply a fraction, what we do is we multiply the numerators then multiply the denominators. So, one multiplied by one is one. Four multiplied by three is 12. So, we’ve got one over 12 or one twelfth to the power of negative one. Well, as we said before, when we’ve got something raised to the power of negative one, what we need to do is just find the reciprocal. And to find the reciprocal, what you do is you flip the numerator and denominator.

So therefore, our two to the power of negative two multiplied by three to the power of negative one all to the power of negative one becomes 12. And that’s because the final step was to have one over 12, or one twelfth, to the power of negative one. Well, the reciprocal of one over 12 is just 12.

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