Basic Mathematics. Trouble with powers.

Greets,

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?

-

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

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

-
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 $$16 \cdot 6 \cdot a^6 \cdot b^{10} = 2^5\cdot 3^1\cdot a^6\cdot b^{10}$$

-
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.

-

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

-

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 $m, n$.

-

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

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 $2^m3^na^rb^s$.
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