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.
