In this question we have a product of two numbers with an exponent.
The numbers are in the form:
[tex]a^b[/tex]Where 'a' is the base of the number and 'b' is the exponent.
In this case, both numbers have the same base (3), so to calculate the product we just need to repeat the base, and the new exponent will be the sum of the exponents:
[tex]3^2\cdot3^4=3^{(2+4)}=3^6[/tex]So the first option is a valid answer.
The second option is not a valid answer, because 3^8 is different from 3^6.
The third option is not a valid answer, because 9^6 is different from 3^6.
To check if the fourth option is a valid answer, we need to calculate it in the same way we did before:
[tex]\begin{gathered} 3^{-4}\cdot3^{10}=3^{(-4+10)}=3^6 \\ \end{gathered}[/tex]The answer is the same we found in the beginning, so the fourth option is also a valid answer.
Fifth option:
[tex]3^0\cdot3^8=3^{(0+8)}=3^8[/tex]The fifth option is not a valid answer.
Sixth option:
[tex]3^3\cdot3^3=3^{(3+3)}=3^6[/tex]The sixth option is a valid answer.
Seventh option:
[tex](3\cdot2)\cdot(3\cdot4)=2\cdot4\cdot3\cdot3=8\cdot3^2[/tex]This value is different from 3^6, so this option is not a valid answer.
Eighth option:
[tex](3\cdot3)\cdot(3\cdot3\cdot3\cdot3)=3^2\cdot3^4=3^{(2+4)}=3^6[/tex]This option is a valid answer.
So the options that apply are:
First, fourth, sixth and eighth.