Step by step
The question
Question: work out 16^(1/4).
16^(1/4)
A fraction power has two jobs.
The bottom number, 4, says which root: the 4th root.
The top number, 1, says which power.
a^(m/n) = (n√a)m
Careful!
The power is not times.
16 times 1/4 is a different number.
Careful: not 16^(1/4) = 16 × 14 ✗
1 Write it as a root
The bottom is 4, so it is the 4th root of 16.
The top is 1: power 1 changes nothing.
= 4√16
The 4th root of 16 is 2, because 2 × 2 × 2 × 2 is 16.
2 × 2 × 2 × 2 = 16
So 16^(1/4) = 2.
= 2
2 Check
Let's check: 2 times itself 4 times.
We get 16.
So the answer is right!
2 × 2 × 2 × 2 = 16
Let's look back.
First: write it as a root.
Last: check.
Answer
= 2