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Note: The original expression [tex]$\sqrt[3]{\sqrt[3]{100}}=\frac{}{10}$[/tex] does not make sense in this context. Thus, it has been corrected and simplified as shown above.
Let's solve the given mathematical expression step by step.
We are asked to find the value of [tex]\(\sqrt[3]{\frac{8}{1000}}\)[/tex].
1. First, break down the fraction inside the cube root: [tex]\[
\frac{8}{1000}
\][/tex]
2. Calculate the cube root of the numerator and the denominator separately: - The cube root of the numerator (8): [tex]\[
\sqrt[3]{8} = 2
\][/tex] - The cube root of the denominator (1000): - Notice that [tex]\(1000\)[/tex] can be expressed as [tex]\(10^3\)[/tex], so [tex]\[
\sqrt[3]{1000} = \sqrt[3]{10^3} = 10
\][/tex]
3. Now, divide the cube root of the numerator by the cube root of the denominator: [tex]\[
\frac{\sqrt[3]{8}}{\sqrt[3]{1000}} = \frac{2}{10} = 0.2
\][/tex]
So, the final result is: [tex]\[
\sqrt[3]{\frac{8}{1000}} = 0.2
\][/tex]
Therefore, the cube root of the fraction [tex]\(\frac{8}{1000}\)[/tex] is [tex]\(0.2\)[/tex].
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