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I don't know why but I just can't simplify this expression and its driving me mad!! Could someone please help me with the steps?

$\frac {2^n 9^{2n+1}}{6^{n-2}}$

I know the answer is 4 x $3^{3n + 4}$ I just can't get there.

Thanks in advance :)

Dani
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2 Answers2

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Notice that:

$$6^{n-2}=2^{n-2}3^{n-2}$$

and

$$9^{2n+1}=3^{4n+2}$$

Then use exponent rules.

user71352
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  • Thank you!!! Can do it now. Couldn't see that step by myself. Much appreciated. – Dani Aug 04 '14 at 05:00
  • You're welcome!!! Glad you are able to solve the problem now. – user71352 Aug 04 '14 at 05:00
  • Oh no I still can't get it!!!

    I've done:

    $\frac {2^{n} 3^{4n+2}}{2^{n} 3^{4n} 3^{n} 3^{-2}}$

    $ \frac {2^{n} 3^{4n} 3^{2} 2^{2} 3^{2}}{2^{n} 3^{n}}$

    $ \frac {2^{n}3^{4n}18^{2}}{6^{n}}$

    $ \frac {3^{4n} 18^{2}}{3}$

    I can see this isn't going to lead anywhere useful! Can you please help set me in the right direction a bit more? Thank you

     – Dani Aug 04 '14 at 05:12
  • Can you show me what you are getting? – user71352 Aug 04 '14 at 05:15
  • Ok the denominator on that first one should say $2^{n} 2^{-2} 3^{n} 3^{-2}$ – Dani Aug 04 '14 at 05:19
  • Yes that should be the denominator. So we have: $\frac{2^{n}3^{4n+2}}{2^{n-2}3^{n-2}}$. Now we can use that $\frac{a^{b}}{a^{b}}=a^{b-c}$ to simplify. – user71352 Aug 04 '14 at 05:25
  • Oh right!!!!! I'm so silly. Thank you so much I've got it. THANK YOU! :) – Dani Aug 04 '14 at 05:29
  • No worries. Glad you understand now. YOU'RE WELCOME! – user71352 Aug 04 '14 at 05:30
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$$\frac {2^n 9^{2n+1}}{6^{n-2}}$$ $$\frac {2^n 3^{4n+2}}{2^{n-2}3^{n-2}}$$ $$2^{(n)-(n-2)}3^{(4n+2)-(n-2)}=4*3^{3n+4}$$

Shabbeh
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