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].
