Step by step
The question
Question: work out 4^(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.
4 times 3/2 is a different number.
1 Take the root
The bottom is 2: the square root of 4.
The top is 3: to the power 3.
We take the root first.
It keeps the numbers small.
√4 is 2, because 2 × 2 is 4.
We write 2 in place of √4.
2 Take the power
2 to the power 3 is 2 × 2 × 2.
That is 8.
So 4^(3/2) = 8.
3 Check
Let's check the other way: the power first, then the root.
4 to the power 3 is 64.
The square root of 64 is 8, because 8 × 8 is 64.
We get 8 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.