Certainly! Let's simplify the expression [tex]\(\frac{f^9 h^{23}}{f^3 h^{17}}\)[/tex] step-by-step in a clear and methodical manner.
1. Identify the original expression:
[tex]\[
\frac{f^9 h^{23}}{f^3 h^{17}}
\][/tex]
2. Simplify the [tex]\(f\)[/tex]-terms:
[tex]\[
\frac{f^9}{f^3} = f^{9-3} = f^6
\][/tex]
Explanation: When dividing powers with the same base, subtract the exponents.
3. Simplify the [tex]\(h\)[/tex]-terms:
[tex]\[
\frac{h^{23}}{h^{17}} = h^{23-17} = h^6
\][/tex]
Explanation: Similar to the [tex]\(f\)[/tex]-terms, subtract the exponents for [tex]\(h\)[/tex]-terms as well.
4. Combine the simplified [tex]\(f\)[/tex]-terms and [tex]\(h\)[/tex]-terms:
[tex]\[
f^6 h^6
\][/tex]
Thus, the correct simplification of the expression [tex]\(\frac{f^9 h^{23}}{f^3 h^{17}}\)[/tex] is:
[tex]\[
f^6 h^6
\][/tex]
Among the given options, the correct choice is:
[tex]\[
\boxed{f^6 h^6}
\][/tex]
