Step by step
The question
Question: work out 8^(1/3).
8^(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.
8 times 1/3 is a different number.
Careful: not 8^(1/3) = 8 × 13 ✗
1 Write it as a root
The bottom is 3, so it is the cube root of 8.
The top is 1: power 1 changes nothing.
= 3√8
∛8 is 2, because 2 × 2 × 2 is 8.
2 × 2 × 2 = 8
So 8^(1/3) = 2.
= 2
2 Check
Let's check: 2 times itself 3 times.
We get 8.
So the answer is right!
2 × 2 × 2 = 8
Let's look back.
First: write it as a root.
Last: check.
Answer
= 2