Certainly, let's simplify the given expression [tex]\(\frac{g^5 h^4}{g^2 h^3}\)[/tex] step by step.
1. Look at the variables [tex]\(g\)[/tex]:
[tex]\[\frac{g^5}{g^2}\][/tex]
Using the laws of exponents, specifically [tex]\(a^m / a^n = a^{m-n}\)[/tex]:
[tex]\[g^{5-2} = g^3\][/tex]
2. Next, look at the variables [tex]\(h\)[/tex]:
[tex]\[\frac{h^4}{h^3}\][/tex]
Again applying the laws of exponents:
[tex]\[h^{4-3} = h\][/tex]
3. Combine the simplified parts:
[tex]\[\frac{g^5 h^4}{g^2 h^3} = g^3 \cdot h\][/tex]
Given the options:
- [tex]\(g^3 h\)[/tex]
- [tex]\(g^7 h\)[/tex]
- [tex]\(g^7 h^7\)[/tex]
- [tex]\(\frac{g^3}{h^7}\)[/tex]
The correct simplification of the expression [tex]\(\frac{g^5 h^4}{g^2 h^3}\)[/tex] is:
[tex]\[g^3 h\][/tex]
Thus, the correct answer is:
[tex]\[g^3 h\][/tex]
