# Expressing $16b^3a^2(6ab^4)(ab)^3$ in the form $2^m3^na^rb^s$

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

Express the following expression in the form $$2^m3^na^rb^s$$, where $$m, n, r, s$$ are positive integers:$$16b^3a^2(6ab^4)(ab)^3$$

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. May 8, 2013 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 May 9, 2013 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. May 9, 2013 at 2:22
• It's just \cdot for formatting "$\cdot$" May 9, 2013 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 $32\cdot 3$.

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. May 9, 2013 at 2:37