Question

Select all the expressions that are equivalent to (2)^n+³

Answer 1

Answer:

The expressions which equivalent to  $(2)^{n+3}$ are:

$4(2)^{n+1}$  ⇒ B

$8(2)^{n}$ ⇒ C

Step-by-step explanation:

Let us revise some rules of exponent

• $a^{m}$ × $a^{m}$  = $a^{m+n}$
• $(a^{m})^{n}$ = $a^{m*n}$

Now let us find the equivalent expressions of  $(2)^{n+3}$

A.

∵ 4 = 2 × 2

∴ 4 =  $2^{2}$

∴  $(4)^{n+2}$ =  $(2^{2})^{n+2}$

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

∵ 2(n + 2) = 2n + 4

∴  $(4)^{n+2}$ =  $(2)^{2n+4}$  

B.

∵ 4 = 2 × 2

∴ 4 =  2²

∴  $4(2)^{n+1}$ = 2² ×  $(2)^{n+1}$

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

∵ 2 + n + 1 = n + 3

∴   $4(2)^{n+1}$ =  $(2)^{n+3}$

C.

∵ 8 = 2 × 2 × 2

∴ 8 =  2³

∴  $8(2)^{n}$ = 2³ ×  $(2)^{n}$

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

∵ 3 + n = n + 3

∴  $8(2)^{n}$ =  $(2)^{n+3}$

D.

∵ 16 = 2 × 2 × 2 × 2

∴ 16 = $2^{4}$

∴  $16(2)^{n}$ = $2^{4}$  ×  $(2)^{n}$

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

∵ 4 + n = n + 4

∴  $16(2)^{n}$ =  $(2)^{n+4}$

E.

$(2)^{2n+3}$ is in its simplest form

The expressions which equivalent to  $(2)^{n+3}$ are:

$4(2)^{n+1}$  ⇒ B

$8(2)^{n}$ ⇒ C