Video Transcript
If 𝑥 equals root two, find 𝑥
to the negative fourth power.
Let’s start by substituting 𝑥
equals root two into 𝑥 to the negative fourth power. Now, to calculate root two to
the negative fourth power, we can apply the law for negative exponents. That is, 𝑎 to the negative
𝑛th power equals one over 𝑎 to the 𝑛th power, where 𝑎 is in the set of real
numbers without zero and 𝑛 is an integer. So this tells us that we can
write root two to the negative fourth power as one over root two to the fourth
power.
Now, root two to the fourth
power is something we can calculate. Let’s expand this power. We know that evaluating a power
means that we multiply the base by itself 𝑛 times. So root two to the fourth power
is the same as root two multiplied by root two multiplied by root two multiplied
by root two.
At this point, we can recall
the rule that root 𝑎 multiplied by root 𝑎 is just 𝑎 for 𝑎 greater than
zero. Therefore, we can simplify this
to be two multiplied by two, and that just gives us four. So our denominator is four, and
our answer is therefore one over four.
