Video Transcript
Simplify one over root two to the power of negative one.
The expression we’ve been asked to simplify contains a power of the base root two in the denominator of a unit fraction. As the power is negative, we can recall the law for negative exponents, which states for a nonzero real base 𝑎, 𝑎 to the power of negative 𝑛 is equal to one over 𝑎 to the 𝑛th power. So, root two to the power of negative one is equal to one over root two to the first power. But of course, any value to the first power is just equal to that value itself, so this simplifies to one over root two.
Considering the original expression, we can now say that one over root two to the power of negative one is equal to one divided by one over root two. Dividing by a fraction is equivalent to multiplying by its reciprocal. So the expression becomes one multiplied by root two over one. Multiplying and dividing by one have no effect on a value, so this simplifies to root two.
So, by recalling the law for negative exponents, we’ve found that the simplified form of the given expression is root two.
