Question

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

Answer 1

C.),F.),andD.) Are correct

Explanation:

Answer 2

Option: C, D and F are the correct options.

C.
`((36)/(4))^x`

D.
`9\cdot 9^(x-1)`

F.
`(36^x)/(4^x)`

Explanation:

We are asked to find the expression which is equivalent to:

`9^x`

C)

`((36)/(4))^x`

We know that:

`((36)/(4))^x=9^x`

Since, 36/4=9

Hence, option: C is correct.

D)

`9\cdot 9^(x-1)=9^(1+x-1)`

Since,

`a^m\cdot a^n=a^(m+n)`

Hence,

`9\cdot 9^(x-1)=9^x`

Hence, option: D is correct.

F)

`(36^x)/(4^x)`

We know that:

`(36^x)/(4^x)=((36)/(4))^x`

Since, we know that:

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

Hence, we have:

`(36^x)/(4^x)=9^x`

Since, 36/4=9

Hence, option: F is the correct answer.