Step by step
The question
Question: work out 16^(3/4).
A fraction power has two jobs.
The bottom number, 4, says which root: the 4th root.
The top number, 3, says which power.
Careful!
The power is not times.
16 times 3/4 is a different number.
1 Take the root
The bottom is 4: the 4th root of 16.
The top is 3: to the power 3.
We take the root first.
It keeps the numbers small.
The 4th root of 16 is 2, because 2 × 2 × 2 × 2 is 16.
We write 2 in place of the 4th root of 16.
2 Take the power
2 to the power 3 is 2 × 2 × 2.
That is 8.
So 16^(3/4) = 8.
3 Check
Let's check the other way: the power first, then the root.
16 to the power 3 is 4096.
The 4th root of 4096 is 8, because 8 × 8 × 8 × 8 is 4096.
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.