Answer:
The expressions which equivalent to [tex](2)^{n+3}[/tex] are:
[tex]4(2)^{n+1}[/tex] ⇒ B
[tex]8(2)^{n}[/tex] ⇒ C
Step-by-step explanation:
Let us revise some rules of exponent
Now let us find the equivalent expressions of [tex](2)^{n+3}[/tex]
A.
∵ 4 = 2 × 2
∴ 4 = [tex]2^{2}[/tex]
∴ [tex](4)^{n+2}[/tex] = [tex](2^{2})^{n+2}[/tex]
- By using the second rule above multiply 2 and (n + 2)
∵ 2(n + 2) = 2n + 4
∴ [tex](4)^{n+2}[/tex] = [tex](2)^{2n+4}[/tex]
B.
∵ 4 = 2 × 2
∴ 4 = 2²
∴ [tex]4(2)^{n+1}[/tex] = 2² × [tex](2)^{n+1}[/tex]
- By using the first rule rule add the exponents of 2
∵ 2 + n + 1 = n + 3
∴ [tex]4(2)^{n+1}[/tex] = [tex](2)^{n+3}[/tex]
C.
∵ 8 = 2 × 2 × 2
∴ 8 = 2³
∴ [tex]8(2)^{n}[/tex] = 2³ × [tex](2)^{n}[/tex]
- By using the first rule rule add the exponents of 2
∵ 3 + n = n + 3
∴ [tex]8(2)^{n}[/tex] = [tex](2)^{n+3}[/tex]
D.
∵ 16 = 2 × 2 × 2 × 2
∴ 16 = [tex]2^{4}[/tex]
∴ [tex]16(2)^{n}[/tex] = [tex]2^{4}[/tex] × [tex](2)^{n}[/tex]
- By using the first rule rule add the exponents of 2
∵ 4 + n = n + 4
∴ [tex]16(2)^{n}[/tex] = [tex](2)^{n+4}[/tex]
E.
[tex](2)^{2n+3}[/tex] is in its simplest form
The expressions which equivalent to [tex](2)^{n+3}[/tex] are:
[tex]4(2)^{n+1}[/tex] ⇒ B
[tex]8(2)^{n}[/tex] ⇒ C
