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Can anyone answer this question? $$3^{n+2} + (3^{n+3} - 3^{n+1})= ?$$

I really want to know how to solve this one, our solution can't seem to agree with the problem's answer thank you!

lioness99a
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yllika
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    This is very hard to read. Do you mean $3^{n+2}+(3^{n+3}-3^{n+1})$? – lulu Mar 22 '17 at 11:39
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    If lulu's comment is correct then it should be $$9 (3^n)+27 (3^n)-3 (3^n)=33 (3^n)$$ – Juniven Acapulco Mar 22 '17 at 11:40
  • Something that may help $3^{n+2} = 3^n3^2$. – Rumplestillskin Mar 22 '17 at 11:45
  • Yes that's the question.Thank you! Can I follow up? that is most of us answered after trying to solve but we're all confused because the question's answer is a fraction whicg is 3/8.maybe you could figure this one out? Thank you! – yllika Mar 22 '17 at 11:45
  • If the answer is three eights something is missing from the question. Either there should be right side or information about n or something like that. – DRF Mar 22 '17 at 11:57
  • yes somehow you are correct and it does feel something is missing because we can't get that three eights. – yllika Mar 22 '17 at 12:05

1 Answers1

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If the answer is $3/8$ probably the question is:

$$\frac{3^{n+2}}{3^{n+3}-3^{n+1}}=\frac{3^2\cdot3^n}{3^3\cdot3^{n}-3\cdot3^{n}}=\frac{3^2\cdot3^n}{3^n(3^3-3)}=\frac{3^2}{27-3}=\frac{3}{8}$$

Arnaldo
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  • If it's a typo error in the examiners part,then I can accept this statement of yours sir. It didn't even cross our minds of the possibility of it to be in division.thank you! – yllika Mar 22 '17 at 12:08
  • @yllika: I'm pretty sure that there is a typo. You are welcome! – Arnaldo Mar 22 '17 at 12:13
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    @ylilka note also that the division symbol $\div$ can look like a plus especially if some copying was done. – DRF Mar 22 '17 at 12:33
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    @DRF: I thought the same thing! – Arnaldo Mar 22 '17 at 12:38
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    @yllika If you look very closely at the image, you can see that the symbol looks a little different from the $+$ signs you can see in the exponents. So it's a $\div$, but horrible typesetting/copying quality obscures that. [One more reason to avoid $\div$ and use the clear $\frac{a}{b}$ instead.] – Daniel Fischer Mar 22 '17 at 13:35
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    @DanielFischer I've had many talks with elementary school teachers about the division sign. Professional mathematicians never use it; they always write fractions. It's sad that kids waste time on it. – Ethan Bolker Mar 22 '17 at 13:35
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    @EthanBolker If the kids wasted time on it, that'd be their own problem. The problem is that teachers waste the children's time with it. [But in their defence, the teachers are probably forced to do that by rules.] – Daniel Fischer Mar 22 '17 at 13:38
  • @DanielFischer Indeed. The teachers often agree with me but we both understand they're not free to change too much. They can alter emphasis and provide alternatives. – Ethan Bolker Mar 22 '17 at 13:42
  • @DanielFischer thank you. I will really keep that in mind. In my previous copies,it does look like a division sign but then in the newer versions,the one like it was re-typed it was a clear addition sign. Can't blame them I guess we just have to adjust to them and read very carefully to derive the correct solution. anyway thank you so much! This helped a lot. – yllika Mar 23 '17 at 03:14