Step by step
The question
Question: work out 25^(−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!
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.
So 25^(−3/2) is 1/25^(3/2).
2 Take the root
The bottom is 2: the square root of 25.
The top is 3: to the power 3.
We take the root first.
It keeps the numbers small.
√25 is 5, because 5 × 5 is 25.
We write 5 in place of √25.
3 Take the power
5 to the power 3 is 5 × 5 × 5.
That is 125.
So 25^(−3/2) = 1/125.
4 Check
Let's check.
Without the minus, 25^(3/2) is 125.
A power times its minus power is 25 to the power 0, which is 1.
125 times 1/125 is 1.
So the answer is right!
Let's look back.
First: remove the minus.
Then: take the root.
Then: take the power.
Last: check.