Explanation
We must find the equivalent expressions to:
[tex]81^x.[/tex]
We will rewrite each expression to check its equivalency.
A. Using the fact that 9 * 9 = 81, we have:
[tex]\lparen9\cdot9)^x=81^x\text{ \checkmark}[/tex]
B. Using the distributive property for powers, we have:
[tex]9^x\cdot9^x=\lparen9\cdot9)^x=81^x\text{ \checkmark}[/tex]
C. Taking into account point B, we see that:
[tex]9\cdot9^x\ne9^x\cdot9^x=81^x\text{ ^^^^2716}[/tex]
D. Taking into account point B, we see that:
[tex]9^2\cdot9^x\ne9^x\cdot9^x=81^{x\text{ }}✖[/tex]
E. Taking into account point B, we see that:
[tex]9\cdot9^{2x}=9\cdot9^x\cdot9^x\ne9^x\cdot9^x=81^x\text{ ^^^^2716}[/tex]
F. Rewriting the expression, we see that:
[tex]9^{2x}=(9^2)^x=81^x\text{ \checkmark}[/tex]Answer
The equivalent expressions are A, B and F.
