Step by step
The question
Question: work out 100^(1/2).
100^(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!
The power is not times.
100 times 1/2 is a different number.
Careful: not 100^(1/2) = 100 × 12 ✗
1 Write it as a root
The bottom is 2, so it is the square root of 100.
The top is 1: power 1 changes nothing.
= √100
√100 is 10, because 10 × 10 is 100.
10 × 10 = 100
So 100^(1/2) = 10.
= 10
2 Check
Let's check: 10 times itself 2 times.
We get 100.
So the answer is right!
10 × 10 = 100
Let's look back.
First: write it as a root.
Last: check.
Answer
= 10