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Simplify Base - question re. one of the Flashcards from here

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Simplify Base - question re. one of the Flashcards from here

by freezing » Sun Jul 26, 2009 3:49 am
Hi everyone,

I'm struggling with one of the awesome flashcards I downloaded here (thanks for those!).

It's called Simplify base (on page 70).

If 27^n = 9^4
Then (3^3)^n = (3^2)^4 => n = 8/3

I understand how to get from the first line to the second part. However, I don't understand how to get from there to n = 8/3. Could anyone help me out with this?

I'm noticing I have problems with these types of problems in general - questions involving powers and simplifying those. Any suggestions on where I might find help with that? (Preferably online, but I'm willing to buy books as well if needed)

Thanks in advance!
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by shibal » Sun Jul 26, 2009 5:37 am
step-by-step... hope it helps....

27=3*3*3=3^3
9=3*3=3^2

3^3n=3^8
3n=8
n=8/3


don't forget that when we have 3^3^n we multiply 3and n, becoming 3n... so for 3^2^4 it's actually 3^4*2= 3^8
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by freezing » Sun Jul 26, 2009 5:48 am
Thank you shibal!

Yes, this helps. I didn't think about multiplying these, I somehow always get stuck there.
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