Question

Which expressions are equivalent to the one below? Check all that apply.A.3xB.C.D.(21 - 7)xE.3x-7F.3

Answer 1

A, B, and C

Step-by-step explanation

We want to find the expressions that are equivalent to the given expression:

`(21^x)/(7^x)`

First, let us simplify the given expression using the following law of exponents:

`(a^c)/(b^c)=((a)/(b))^c`

Therefore, we have that the expression becomes:

`(21^x)/(7^x)=((21)/(7))^x=3^x`

Another way of simplifying the expression is to simplify the numerator using the following law of exponents:

`(a*b)^x=a^x*b^x`

Therefore, the expression becomes:

`\begin{gathered} (21^x)/(7^x)=((7*3)^x)/(7^x) \\ \\ \Rightarrow(7^x*3^x)/(7^x) \\ \\ \Rightarrow3^x \end{gathered}`

Therefore, we see that the expressions that are equivalent to the given one are:

`\begin{gathered} 3^x \\ \\ (7^x*3^x)/(7^x) \\ \\ ((21)/(7))^x \end{gathered}`

The correct options are A, B, and C.