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!
A minus in the power does not make the answer negative.
It means 1 over.
Careful: not 8^(−1/3) = −2 ✗
1 Remove the minus
A minus power means 1 over the same power without the minus.
a−n = 1an
So 8^(−1/3) is 1/8^(1/3).
= 18^(1/3)
2 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.
= 13√8
∛8 is 2, because 2 × 2 × 2 is 8.
2 × 2 × 2 = 8
So 8^(−1/3) = 1/2.
= 12
3 Check
Let's check.
Without the minus, 8^(1/3) is 2.
A power times its minus power is 8 to the power 0, which is 1.
8^(1/3) = 2, 80 = 1
2 times 1/2 is 1.
So the answer is right!
2 × 12 = 1
Let's look back.
First: remove the minus.
Then: write it as a root.
Last: check.
Answer
= 12