# Thread: A quick algebra exercise

1. ## A quick algebra exercise

$3^{x+1} + 3^{x+2}$

How do I simplify this?

2. Originally Posted by klik11
$3^{x+1} + 3^{x+2}$

How do I simplify this?

$3^{x+1} + 3^{x+2 } = 3 \cdot 3^x + 3^2 \cdot 3^x = 3^x ( 3 + 3^2 ) = 3^x \cdot (3+9 ) = 3^x \cdot 12$

3. I'm Sorry, I forgot to say that the book says that the answer is
$12*3^{x}$

Could you show me the way to get to that answer?

Edit: I also think you are wrong because it would have been your answer if it there was * and not +.

4. Originally Posted by klik11
I'm Sorry, I forgot to say that the book says that the answer is
$12*3^{x}$

Could you show me the way to get to that answer?
thank you ... lol sorry working so many things at the same time .... I edited that one up there

5. Could you explain me how come

$3 \cdot 3^x + 3^2 \cdot 3^x = 3^x ( 3 + 3^2 )$

6. Originally Posted by klik11
Could you explain me how come

$3 \cdot 3^x + 3^2 \cdot 3^x = 3^x ( 3 + 3^2 )$
okay ...

$3^2 = 3^1 \cdot 3^1$

so

$3^{x+1} = 3^x \cdot 3^1$

now you can write

$3 \cdot 3^x + 3^2 \cdot 3^x$

here you see both of them have common $3^x$ so you can pull it out ...

$yx +2x = x (y+2 )$

same thing

$3 \cdot 3^x + 3^2 \cdot 3^x = 3^x ( 3 + 3^2 )$

7. Remember that a^x * a^y = a^(x+y) and (a^x)^y = a^(xy)