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In Chapter 1.3, Basic Mathematics, Serge Lang, there is the question:

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

b) $16b^3a^2(6ab^4)(ab)^3$

The answer I got was $16 \cdot 6 \cdot a^6 \cdot b^{10}$.

Is there something I did wrong?

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up vote 4 down vote accepted

You're on the right track, just not quite finished:

$16*6=2^4 * 2 * 3=2^5 * 3^1$

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Now I get it. I struggled with that one for a while there.. will +1 when I have enough rep. – usernvk May 8 '13 at 23:30

What you've done so far is correct... but we need to do a little more...

$$16 \times 6 = 2^4\times 2 \times 3 = 2^5 \times 3$$

So we have that $$16 \cdot 6 \cdot a^6 \cdot b^{10} = 2^5\cdot 3^1\cdot a^6\cdot b^{10}$$

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Deserves a thumbs up! +1 – Amzoti May 9 '13 at 0:31
Great answer, except the working shows $2^5$ but concluded $2^4$. +1. Also, thanks for the $\cdot$ edit. Couldn't figure out where to find the symbol. – usernvk May 9 '13 at 2:22
It's just \cdot for formatting "$\cdot$" – amWhy May 9 '13 at 2:27

Yes, $16\cdot 6$ is not yet in the form $2^m\cdot 3^n$. Otherwise it is correct.

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$6$ isn't a power of $3$. You'll want to change $16\cdot 6$ to $32\cdot 3$.

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Everything is correct, except you should express 16*6 as $2^{m}3^{n}$ as suggested. My hint is to split it up as $16*6 = 32*3$, which can easily be expressed as $2^{m}3^{n}$ for some $m, n$.

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Great question, believe it or not, these same questions from that same book stumped me at one point.

This might help you out.

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

The goal here is to reduce everything to it's smallest factors. In these questions they all reduce to smallest factors in the form $2^m3^na^rb^s$.

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When I couldn't figure out what the exercise was asking, your question was indispensable. That helped me solve (a) but (b) had me stumped. I couldn't figure out how to reduce $16 \cdot 6$ to $2^m \cdot 3^n$. +1 on your original question. – usernvk May 9 '13 at 2:37

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