Step by step
The question
Question: work out 64^(−2/3).
A fraction power has two jobs.
The bottom number, 3, says which root: the cube root.
The top number, 2, says which power.
Careful!
A minus in the power does not make the answer negative.
It means 1 over.
1 Remove the minus
A minus power means 1 over the same power without the minus.
So 64^(−2/3) is 1/64^(2/3).
2 Take the root
The bottom is 3: the cube root of 64.
The top is 2: to the power 2.
We take the root first.
It keeps the numbers small.
∛64 is 4, because 4 × 4 × 4 is 64.
We write 4 in place of ∛64.
3 Take the power
4 to the power 2 is 4 × 4.
That is 16.
So 64^(−2/3) = 1/16.
4 Check
Let's check.
Without the minus, 64^(2/3) is 16.
A power times its minus power is 64 to the power 0, which is 1.
16 times 1/16 is 1.
So the answer is right!
Let's look back.
First: remove the minus.
Then: take the root.
Then: take the power.
Last: check.