Question

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

Answer 1

Answer: The correct options are

(B)
`(9^x.3^x)/(9^x)`

(C)
`3^x`

(E)
`\left((27)/(9)\right)^3.`

Step-by-step explanation: The given expression is

`E=(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)~(a^x)/(b^x)=\left((a)/(b)\right)^x.`

We have

`E\\\\\\=(27^x)/(9^x)\\\\\\=((9* 3)^x)/(9^x)\\\\\\=(9^x.3^x)/(9^x)\\\\\\=3^x.`

Also,

`E=(27^x)/(9^x)=\left((27)/(9)\right)^x.`

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