Step by step
The question
Question: work out 16^(−1/2).
A power that is a fraction is called a rational exponent.
It has two jobs.
The bottom number, 2, says which root: the square root.
The top number, 1, says which power.
For the square root, the small 2 is not written.
Why a root?
When we multiply powers of the same number, we add the powers.
16 to the power 1/2, multiplied 2 times: the powers add up to 1.
So it makes 16 to the power 1, which is 16.
That is what the square root of 16 does.
Careful!
A minus in the power does not make the answer negative.
It means 1 over.
1 Remove the minus
A minus power means 1 over the same power without the minus, like in the exponent lesson: 2 to the power −1 is 1/2.
So 16^(−1/2) is 1/16^(1/2).
2 Write it as a root
The bottom is 2, so it is the square root of 16.
The top is 1: power 1 changes nothing.
√16 is 4, because 4 × 4 is 16.
So 16^(−1/2) = 1/4.
3 Check
Let's check.
Without the minus, 16^(1/2) is 4.
A power times its minus power is 16 to the power 0, which is 1.
4 times 1/4 is 1.
So the answer is right!
Let's look back.
First: remove the minus.
Then: write it as a root.
Last: check.