Step by step
The question
Question: work out 9^(3/2).
A fraction power has two jobs.
The bottom number, 2, says which root: the square root.
The top number, 3, says which power.
For the square root, the small 2 is not written.
Careful!
The power is not times.
9 times 3/2 is a different number.
1 Take the root
The bottom is 2: the square root of 9.
The top is 3: to the power 3.
We take the root first.
It keeps the numbers small.
√9 is 3, because 3 × 3 is 9.
We write 3 in place of √9.
2 Take the power
3 to the power 3 is 3 × 3 × 3.
That is 27.
So 9^(3/2) = 27.
3 Check
Let's check the other way: the power first, then the root.
9 to the power 3 is 729.
The square root of 729 is 27, because 27 × 27 is 729.
We get 27 again.
But the numbers were bigger.
So root first is easier.
And the answer is right!
Let's look back.
First: take the root.
Then: take the power.
Last: check.