Step by step
The question
Question: work out 9^(−1/2).
9^(−1/2)
A fraction power 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.
a^(m/n) = (n√a)m
Careful!
A minus in the power does not make the answer negative.
It means 1 over.
Careful: not 9^(−1/2) = −3 ✗
1 Remove the minus
A minus power means 1 over the same power without the minus.
a−n = 1an
So 9^(−1/2) is 1/9^(1/2).
= 19^(1/2)
2 Write it as a root
The bottom is 2, so it is the square root of 9.
The top is 1: power 1 changes nothing.
= 1√9
√9 is 3, because 3 × 3 is 9.
3 × 3 = 9
So 9^(−1/2) = 1/3.
= 13
3 Check
Let's check.
Without the minus, 9^(1/2) is 3.
A power times its minus power is 9 to the power 0, which is 1.
9^(1/2) = 3, 90 = 1
3 times 1/3 is 1.
So the answer is right!
3 × 13 = 1
Let's look back.
First: remove the minus.
Then: write it as a root.
Last: check.
Answer
= 13