Step by step
The question
Question: work out 32^(1/5).
32^(1/5)
A fraction power has two jobs.
The bottom number, 5, says which root: the 5th root.
The top number, 1, says which power.
a^(m/n) = (n√a)m
Careful!
The power is not times.
32 times 1/5 is a different number.
Careful: not 32^(1/5) = 32 × 15 ✗
1 Write it as a root
The bottom is 5, so it is the 5th root of 32.
The top is 1: power 1 changes nothing.
= 5√32
The 5th root of 32 is 2, because 2 × 2 × 2 × 2 × 2 is 32.
2 × 2 × 2 × 2 × 2 = 32
So 32^(1/5) = 2.
= 2
2 Check
Let's check: 2 times itself 5 times.
We get 32.
So the answer is right!
2 × 2 × 2 × 2 × 2 = 32
Let's look back.
First: write it as a root.
Last: check.
Answer
= 2