Step by step
The question
Question: work out 125^(1/3).
125^(1/3)
A fraction power has two jobs.
The bottom number, 3, says which root: the cube root.
The top number, 1, says which power.
a^(m/n) = (n√a)m
Careful!
The power is not times.
125 times 1/3 is a different number.
Careful: not 125^(1/3) = 125 × 13 ✗
1 Write it as a root
The bottom is 3, so it is the cube root of 125.
The top is 1: power 1 changes nothing.
= 3√125
∛125 is 5, because 5 × 5 × 5 is 125.
5 × 5 × 5 = 125
So 125^(1/3) = 5.
= 5
2 Check
Let's check: 5 times itself 3 times.
We get 125.
So the answer is right!
5 × 5 × 5 = 125
Let's look back.
First: write it as a root.
Last: check.
Answer
= 5