Step by step
The question
Question: solve x³ = 1/64.
x3 = 164
x³ means x times x times x.
We want just x.
x³ = x × x × x
1 Cube root of both sides
The cube root asks: which number, times itself three times, makes this?
∛27 = ? → ? × ? × ? = 27
The cubes: 1 times 1 times 1 is 1.
2 times 2 times 2 is 8.
3 times 3 times 3 is 27.
4 times 4 times 4 is 64.
1³ = 1, 2³ = 8, 3³ = 27, 4³ = 64
x is the cube root of 1/64.
x = 3√164
We take the cube root of the top and of the bottom.
1 cubed is 1.
4 cubed is 64.
x = 3√13√64
So x = 1/4.
x = 14
Careful!
A cube has one answer, not two.
Minus 1/4, cubed, is minus 1/64.
Not like x² = 49.
Careful: not x = 14 or x = −14 ✗
2 Check
Let's check: 1/4 times 1/4 times 1/4 is 1/64.
14 × 14 × 14 = 164
The same as the right side.
So the answer is right!
Let's look back.
First: cube root of both sides.
Last: check.
Answer
Careful: not x = 14 or x = −14 ✗