The given expression is:
[tex]\[
\frac{f^9 h^{23}}{f^3 h^{17}}
\][/tex]
To simplify this, we need to apply the properties of exponents. Specifically, we will use the property that [tex]\(\frac{a^m}{a^n} = a^{m-n}\)[/tex].
Start by simplifying the exponent for [tex]\(f\)[/tex]:
[tex]\[
\frac{f^9}{f^3} = f^{9-3} = f^6
\][/tex]
Next, simplify the exponent for [tex]\(h\)[/tex]:
[tex]\[
\frac{h^{23}}{h^{17}} = h^{23-17} = h^6
\][/tex]
Putting it all together, we get:
[tex]\[
\frac{f^9 h^{23}}{f^3 h^{17}} = f^6 h^6
\][/tex]
Therefore, the correct simplification of [tex]\(\frac{f^9 h^{23}}{f^3 h^{17}}\)[/tex] is:
[tex]\[
f^6 h^6
\][/tex]
So the correct answer is:
[tex]\[
f^6 h^6
\][/tex]
