Certainly! Let's break down the expression [tex]\(\frac{5 \sqrt[3]{4}}{2 \sqrt[3]{25}}\)[/tex] step by step.
1. Identify the numerator and denominator:
- The numerator is [tex]\(5 \sqrt[3]{4}\)[/tex].
- The denominator is [tex]\(2 \sqrt[3]{25}\)[/tex].
2. Calculate the cube roots individually:
- Find [tex]\(\sqrt[3]{4}\)[/tex]: This is the cube root of 4.
- Find [tex]\(\sqrt[3]{25}\)[/tex]: This is the cube root of 25.
3. Simplify the numerator:
- Multiply 5 by [tex]\(\sqrt[3]{4}\)[/tex]:
[tex]\[
5 \sqrt[3]{4}
\][/tex]
The numerical result is approximately [tex]\(7.937005259840997\)[/tex].
4. Simplify the denominator:
- Multiply 2 by [tex]\(\sqrt[3]{25}\)[/tex]:
[tex]\[
2 \sqrt[3]{25}
\][/tex]
The numerical result is approximately [tex]\(5.848035476425732\)[/tex].
5. Divide the simplified numerator by the simplified denominator:
[tex]\[
\frac{7.937005259840997}{5.848035476425732} \approx 1.3572088082974532
\][/tex]
Therefore, the simplified value of the expression [tex]\(\frac{5 \sqrt[3]{4}}{2 \sqrt[3]{25}}\)[/tex] is approximately [tex]\(1.3572088082974532\)[/tex].
