Question

Which expressions are equivalent to the one below? Check all that apply. 27^x/9^x

Answer 1

27^x / 9^x
= 3^3x  / 3^2x
= 3^x

So its equivalent to C. 

Its also equivalent to B  and E.

Answer 2

Answer:  The correct options are

(B) $\dfrac{9^x.3^x}{9^x}$

(C) $3^x$

(E) $\left(\dfrac{27}{9}\right)^3.$

Step-by-step explanation:  The given expression is

$E=\dfrac{27^x}{9^x}.$

We are to select the correct expressions that are equivalent to the expression "E".

We will be using the following properties of exponents:

$(i)~a^x.b^x=(ab)^x,\\\\(ii)~\dfrac{a^x}{b^x}=\left(\dfrac{a}{b}\right)^x.$

We have

$E\\\\\\=\dfrac{27^x}{9^x}\\\\\\=\dfrac{(9\times 3)^x}{9^x}\\\\\\=\dfrac{9^x.3^x}{9^x}\\\\\\=3^x.$

Also,

$E=\dfrac{27^x}{9^x}=\left(\dfrac{27}{9}\right)^x.$

Thus, (B), (C) and (E) are the correct options.