Question

Simplify the following
@ganeshie8

Answer 1

\[3^{n+1}-3^{n-1}\]

Answer 2

well you can factor a 3^n out

Answer 3

\[3^n~\times~3^1-3^n~\div~3^1\]

Answer 4

Combining like terms

Answer 5

\[3^n(3-\frac{1}{3})\]

Answer 6

now just find the difference of the fractions in the ( )

Answer 7

\[3^n(\frac{ 8 }{ 3 })\]\[8(3^{n-1}) ?\]

Answer 8

those are both right
I don't know which of the ones you and your teacher find most simplified

Answer 9

what do you mean

Answer 10

we show our work I thought

Answer 11

are you saying the final answer is suppose to be 8(3^(n-1)) ?
if so all you need is quotient rule

Answer 12

\[\frac{3^n}{3}8 =\frac{3^n}{3^1}8 =3^{n-1} 8\]

Answer 13

Thnx @freckles

Answer 14

also here is another way:
\[3^{n+1}-3^{n-1} \\ 3^{n-1+2}-3^{n-1} \\ 3^23^{n-1}-3^{n-1} \\ 9(3^{n-1})-1(3^{n-1}) \text{you have like terms } \\ 8(3^{n-1})\]

Answer 15

either way @MARC_ \[8(3^{n-1})=8 \frac{3^n}{3^1} \text{ by quotient rule } \\ 8 \frac{3^n}{3} \text{ since } 3^1=3 \\ \frac{8}{3} 3^n \]

Answer 16

alright.Thnx @freckles :D