To simplify the expression [tex]\(\frac{g^5 h^4}{g^2 h^3}\)[/tex], we need to deal with the variables [tex]\(g\)[/tex] and [tex]\(h\)[/tex] separately. We'll use the properties of exponents to simplify each part.
1. Simplifying the [tex]\(g\)[/tex] terms:
The given expression has [tex]\(g^5\)[/tex] (in the numerator) and [tex]\(g^2\)[/tex] (in the denominator). Using the property of exponents that [tex]\(\frac{a^m}{a^n} = a^{m-n}\)[/tex]:
[tex]\[
\frac{g^5}{g^2} = g^{5-2} = g^3
\][/tex]
2. Simplifying the [tex]\(h\)[/tex] terms:
The given expression has [tex]\(h^4\)[/tex] (in the numerator) and [tex]\(h^3\)[/tex] (in the denominator). Using the property of exponents that [tex]\(\frac{a^m}{a^n} = a^{m-n}\)[/tex]:
[tex]\[
\frac{h^4}{h^3} = h^{4-3} = h
\][/tex]
3. Combining the simplified terms:
Now we combine the results from simplifying [tex]\(g\)[/tex] and [tex]\(h\)[/tex]:
[tex]\[
\frac{g^5 h^4}{g^2 h^3} = g^3 \cdot h = g^3 h
\][/tex]
Hence, the correct simplification of the expression [tex]\(\frac{g^5 h^4}{g^2 h^3}\)[/tex] is [tex]\(\boxed{g^3 h}\)[/tex].
