Sure, let's work through the given expression step-by-step to simplify it:
The given expression is:
[tex]\[
\frac{1}{4} \cdot \frac{a^{10}}{1} \cdot \frac{1}{b^9}
\][/tex]
### Step 1: Rewrite the fractions
First, let's rewrite the expression in a single fraction:
[tex]\[
\frac{1 \cdot a^{10} \cdot 1}{4 \cdot 1 \cdot b^9}
\][/tex]
This simplifies to:
[tex]\[
\frac{a^{10}}{4b^9}
\][/tex]
### Step 2: Simplify the fraction
The numerator is [tex]\(a^{10}\)[/tex] and the denominator is [tex]\(4b^9\)[/tex]. There is no common factor between [tex]\(a^{10}\)[/tex] and [tex]\(4b^9\)[/tex] that requires further simplification, so the fraction is already in its simplest form.
### Final Answer
Thus, the expression simplifies to:
[tex]\[
\frac{a^{10}}{4b^9}
\][/tex]
There you have it! The given expression has been simplified to:
[tex]\[
\frac{a^{10}}{4b^9}
\][/tex]
