Select all the expressions that are equivalent to (2)^n+³
A. (4)^n+²
B. 4(2)^2+¹
C. 8(2)^n
D. 16(2)^n
E. (2)^2x+³
Please explain as well please

The expressions which equivalent to   are:

 ⇒ B

⇒ C

Step-by-step explanation:

Let us revise some rules of exponent

Now let us find the equivalent expressions of  

A.

∵ 4 = 2 × 2

∴ 4 =  

∴   =  

- By using the second rule above multiply 2 and (n + 2)

∵ 2(n + 2) = 2n + 4

∴   =    

B.

∵ 4 = 2 × 2

∴ 4 =  2²

∴   = 2² ×  

- By using the first rule rule add the exponents of 2

∵ 2 + n + 1 = n + 3

∴   =  

C.

∵ 8 = 2 × 2 × 2

∴ 8 =  2³

∴   = 2³ ×  

- By using the first rule rule add the exponents of 2

∵ 3 + n = n + 3

∴   =  

D.

∵ 16 = 2 × 2 × 2 × 2

∴ 16 =

∴   =  ×  

- By using the first rule rule add the exponents of 2

∵ 4 + n = n + 4

∴   =  

E.

is in its simplest form

The expressions which equivalent to   are:

 ⇒ B

⇒ C

step-by-step explanation: