To tackle this problem, we need to analyze and break down the given algebraic expression: [tex]\( 27y^6 - 8z^3 \)[/tex].
Let's take a detailed, step-by-step look at the components of the expression:
1. Identify the coefficients:
- In the term [tex]\( 27y^6 \)[/tex], the coefficient of [tex]\( y^6 \)[/tex] is [tex]\( 27 \)[/tex].
- In the term [tex]\( 8z^3 \)[/tex], the coefficient of [tex]\( z^3 \)[/tex] is [tex]\( 8 \)[/tex].
2. Identify the variables and their powers:
- The variable [tex]\( y \)[/tex] is raised to the power of [tex]\( 6 \)[/tex] in [tex]\( 27y^6 \)[/tex].
- The variable [tex]\( z \)[/tex] is raised to the power of [tex]\( 3 \)[/tex] in [tex]\( 8z^3 \)[/tex].
Thus, the algebraic expression consists of these two terms: [tex]\( 27y^6 \)[/tex] and [tex]\( 8z^3 \)[/tex].
To rewrite the expression based on the above analysis, simply state:
[tex]\[ 27y^6 - 8z^3 \][/tex]
To summarize:
- The coefficient of [tex]\( y^6 \)[/tex] is [tex]\( 27 \)[/tex].
- The coefficient of [tex]\( z^3 \)[/tex] is [tex]\( 8 \)[/tex].
- The overall expression remains [tex]\( 27y^6 - 8z^3 \)[/tex].
