Sure, let's break the given expression down step-by-step.
Consider the expression [tex]\(\frac{2 a^9}{b^6}\)[/tex].
1. Identify the components:
- The numerator is [tex]\(2 a^9\)[/tex].
- The denominator is [tex]\(b^6\)[/tex].
2. Understand the roles of the variables and constants:
- [tex]\(a\)[/tex] and [tex]\(b\)[/tex] are variables.
- [tex]\(2\)[/tex] is a constant coefficient in the numerator.
3. Exponential notation:
- [tex]\(a^9\)[/tex] means [tex]\(a\)[/tex] raised to the power of 9.
- [tex]\(b^6\)[/tex] means [tex]\(b\)[/tex] raised to the power of 6.
4. Simplify the fraction:
- The fraction [tex]\(\frac{2 a^9}{b^6}\)[/tex] cannot be simplified further if [tex]\(a\)[/tex] and [tex]\(b\)[/tex] are distinct and non-related variables.
Thus, the final simplified form of the expression is:
[tex]\[
\boxed{\frac{2a^9}{b^6}}
\][/tex]
This expression represents the ratio of [tex]\(2a\)[/tex] raised to the ninth power to [tex]\(b\)[/tex] raised to the sixth power.
