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

66 2/3Step-by-step explanation:...

Which expressions are equivalent to the one below?

argarcia255

14.01.2022

The correct options are

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

(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.

0,0(0 оценок)