Answer: 0.1 units
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Work Shown:
0.001 = 1/1000
Apply the cube root to both parts of 1/1000 to get
[tex]\sqrt[3]{1} = 1\\\\\sqrt[3]{1000} = 10[/tex]
So this means that, [tex]\left(\frac{1}{10}\right)^3 = \frac{1}{10}*\frac{1}{10}*\frac{1}{10} = \frac{1}{1000} = 0.001[/tex]
Having a side length of 1/10 = 0.1 unit leads to a volume of 0.001 cubic units.
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A shortcut alternative is to use your calculator to get
[tex](0.001)^{1/3} = 0.1[/tex]
The exponent of 1/3 is the same as a cube root.
