Answer: [tex]GCF=h^4[/tex]
Step-by-step explanation:
You need to remember that:
1) The definition of Greatest common factor (GCF): This is the greatest factor that divides two numbers.
2) The Product of powers property states that:
[tex](a^m)(a^n)=a^{(m+n)}[/tex]
3) To find the Greatest common factor between two numbers, for example, you can descompose them into their prime factors and then choose the commons with the lowest exponent.
In this case, you have [tex]h^4[/tex] and [tex]h^8[/tex]
You can observe that the common base is "h", then you only need to choose the one with the lowest exponent. This is:
[tex]GCF=h^4[/tex]
4) You can also rewrite [tex]h^4[/tex] and [tex]h^8[/tex] as:
[tex]h^4=h*h*h*h\\*h^8=h*h*h*h*h*h*h*h[/tex]
You can observe that the common factor between [tex]h^4[/tex] and [tex]h^8[/tex] is: [tex]h*h*h*h=h^4[/tex]
Then:
[tex]GCF=h*h*h*h=h^4[/tex]
