Question

Which expressions are equivalent to the one below?check all that apply. 21^x/3^x

A.(21-3)^x
B.7
C.7^x
D.(21/3)^x
E.7^x*3^x/3^x
F.3^x

Answer 1

C and E and F are all the correct answers

Answer 2

The equivalent expressions are:

C.

`7^x`

D.

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

E.

`(7^x\cdot 3^x)/(3^x)`

Explanation:

We are asked to find the algebraic expression that is equivalent to the expression:

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

A)

`(21-3)^x`

We know that this expression is incorrect.

Since,
`(a^x)/(b^x)\\eq (a-b)^x`

B)

7

This option is also incorrect.

Since,

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

C)

`7^x`

This option is true.

Since,

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

D)

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

This option is true.

Since,

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

E)

`(7^x\cdot 3^x)/(3^x)`

This option is correct.

Since,

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

F)

`3^x`

This option is incorrect.

Since we get a expression as:

`7^x` but not
`3^x`