Video: Computing Numerical Expressions with Negative Exponents

Which of the following is equal to 4(√6)⁻¹? [A] 24 [B] 2/3 [C] 4√6 [D] (2√6)/3

02:10

Video Transcript

Which of the following is equal to four times the square root of six to the negative one power? A) 24, B) two-thirds, C) four times the square root of six, or D) two times the square root of six over three.

We’re given four times the square root of six to the negative one power. First, we should remember that 𝑥 to the negative 𝑎 power is equal to one over 𝑥 to the 𝑎 power. And this means we could rewrite four times the square root of six to the negative one power as four over the square root of six. But none of our answer choices look like this.

So the next thing we want to do is see if we can get the square root of six out of the denominator. One way to do that is by multiplying this fraction by the square root of six over the square root of six. We know that the value of the square root of six over the square root of six is one. And so we’re not changing the value of this fraction. We’re simply rewriting it. And this process is called rationalising. We’re rationalising the denominator here.

To multiply these fractions, we multiply their numerators, which is four times the square root of six. And in the denominator, we would have the square root of six times the square root of six, which equal six. Four times the square root of six over six is equal to the expression we started with.

But now we notice that we have a numerator and a denominator that’s divisible by two. Four divided by two is two. And six divided by two is three. Which means we can simplify four times the square root of six over six to say two times the square root of six over three, which is option D.

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