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I just recently started relearning math as an adult, this should be easy but I have trouble understanding what the actual question is. I am not just looking for the answer to this, I merely wish to understand what the question is asking.

Express each of the following expressions in the form $2^m3^na^rb^s$, where $m$, $n$, $r$ and $s$ are positive integers.

a) $8a^2b^3(27a^4)(2^5ab)$

$\phantom{\text{ ![a busy cat-miau](}}$

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are you given anywhere that $\gcd(ab,6)=1$, or perhaps that $\gcd(a,b)=1$? – robjohn Jul 16 '12 at 18:07
@robjohn: I think you have to assume that, or that you are solving it for general $a,b$. – Ross Millikan Jul 16 '12 at 18:35
up vote 2 down vote accepted

You are being asked to express $8$ as $2^3$ and similarly $27$, then to commute the various terms to gather the exponents of $2, 3, a, b$. For example, how many powers of $a$ are in the expression?

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7 powers of a? So I get in theory I think what to do, but if I replace 8 with 2 and 27 with 3 but what about the 2^5? Thanks to all who help me! – nitrous2 Jul 16 '12 at 17:49
@nitrous2: Correct. You also need to collect all the factors of $2$, some of which come from the $8$ and some from the $2^5$. – Ross Millikan Jul 16 '12 at 17:54
Okay, so plugging things in I am at $2^m3^na^7b^4$ How do I find the 2^m and 3^n? – nitrous2 Jul 16 '12 at 18:00
The answer is $2^83^3a^7b^4$ How would I of found the 2^m and the 3^n? – nitrous2 Jul 16 '12 at 18:13
So 3^3 is a result of factoring 27? 3*3*3? – nitrous2 Jul 16 '12 at 18:19

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