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

How do I simplify this?

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- Sep 13th 2010, 03:51 AMklik11A quick algebra exercise
$\displaystyle 3^{x+1} + 3^{x+2}$

How do I simplify this? - Sep 13th 2010, 03:57 AMyeKciM
- Sep 13th 2010, 04:00 AMklik11
I'm Sorry, I forgot to say that the book says that the answer is

$\displaystyle 12*3^{x}$

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 +. - Sep 13th 2010, 04:06 AMyeKciM
- Sep 13th 2010, 04:09 AMklik11
Could you explain me how come

$\displaystyle 3 \cdot 3^x + 3^2 \cdot 3^x = 3^x ( 3 + 3^2 )$ - Sep 13th 2010, 04:15 AMyeKciM
okay ...

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

so

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

now you can write

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

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

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

same thing

$\displaystyle 3 \cdot 3^x + 3^2 \cdot 3^x = 3^x ( 3 + 3^2 ) $ - Sep 13th 2010, 05:51 AMWilmer
Remember that a^x * a^y = a^(x+y) and (a^x)^y = a^(xy)