Answer: The correct options are
(B) [tex]\dfrac{9^x.3^x}{9^x}[/tex]
(C) [tex] 3^x[/tex]
(E) [tex]\left(\dfrac{27}{9}\right)^3.[/tex]
Step-by-step explanation: The given expression is
[tex]E=\dfrac{27^x}{9^x}.[/tex]
We are to select the correct expressions that are equivalent to the expression "E".
We will be using the following properties of exponents:
[tex](i)~a^x.b^x=(ab)^x,\\\\(ii)~\dfrac{a^x}{b^x}=\left(\dfrac{a}{b}\right)^x.[/tex]
We have
[tex]E\\\\\\=\dfrac{27^x}{9^x}\\\\\\=\dfrac{(9\times 3)^x}{9^x}\\\\\\=\dfrac{9^x.3^x}{9^x}\\\\\\=3^x.[/tex]
Also,
[tex]E=\dfrac{27^x}{9^x}=\left(\dfrac{27}{9}\right)^x.[/tex]
Thus, (B), (C) and (E) are the correct options.
