Answer :

Certainly! Let's solve the expression [tex]\(\left(m^2 - \frac{1}{8} n\right)^3\)[/tex].

Given the expression:
[tex]\[ \left(m^2 - \frac{1}{8} n\right)^3 \][/tex]

We start by identifying the terms inside the parentheses:
- [tex]\(m^2\)[/tex] is the first term.
- [tex]\(\frac{1}{8} n\)[/tex] is the second term, where the coefficient is [tex]\(\frac{1}{8}\)[/tex].

Combining these terms, we treat the entire expression inside the parentheses as a single entity and raise this entity to the power of 3.

As a detailed step-by-step solution:

1. Identify the terms:
- First term: [tex]\(m^2\)[/tex]
- Second term: [tex]\(\frac{1}{8} n\)[/tex]

2. Expression inside parentheses:
[tex]\[ m^2 - \frac{1}{8} n \][/tex]

3. Raise the entire expression to the power of 3:
[tex]\[ \left(m^2 - \frac{1}{8} n\right)^3 \][/tex]

So, our final simplified expression is:
[tex]\[ (m^2 - 0.125n)^3 \][/tex]

This is the detailed solution for the given expression.