Question

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

49x

A.7*7^x
B.7 * 7^2x
C.7^x * 7^x
D.(7* 7)^x
E.7^2* 7^x
F.7^2x

Answer 1

Answer: C.
`7^x * 7^x`

D.
`(7* 7)^x`

F.
`7^(2x)`

Explanation:

Law of exponents :

`a^m*a^n=a^(m+n)\\(a^m)^n=a^(mn)`

`49^x=(7^2)^x=7^(2x)`

A.
`7*7^x`

`=7^(1+x)\\eq49^x`

B.
`7 * 7^2x`

=
`7^(1+2x)\\eq49^x`

C.
`7^x * 7^x`

`=7^(x+x)=7^(2x)=(7^2)^x=49^x`

D.
`(7* 7)^x`

`=(7^2)^x=49^x`

E.
`7^2* 7^x`

`7^(2+x)\\eq49^x`

F.
`7^(2x)=(7^2)^x=49^x`

Answer 2

The answers are C, D, and F.

The result is 49ˣ

Let's check all choices:
A. 7 * 7ˣ = 7¹ * 7ˣ = 7¹⁺ˣ
B. 7 * 7²ˣ = 7¹ * 7³ˣ = 7¹⁺²ˣ
C. 7ˣ * 7ˣ = 7ˣ⁺ˣ = 7²ˣ = (7²)ˣ = 49ˣ - CORRECT
D. (7 * 7)ˣ = 49ˣ - CORRECT
E. 7² * 7ˣ = 7²⁺ˣ
F. 7²ˣ = (7²)ˣ = 49ˣ - CORRECT