Step by step
The question
Question: work out 27^(1/3).
27^(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.
27 times 1/3 is a different number.
Careful: not 27^(1/3) = 27 × 13 ✗
1 Write it as a root
The bottom is 3, so it is the cube root of 27.
The top is 1: power 1 changes nothing.
= 3√27
∛27 is 3, because 3 × 3 × 3 is 27.
3 × 3 × 3 = 27
So 27^(1/3) = 3.
= 3
2 Check
Let's check: 3 times itself 3 times.
We get 27.
So the answer is right!
3 × 3 × 3 = 27
Let's look back.
First: write it as a root.
Last: check.
Answer
= 3