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I realize that this is basic arithmetic, but I really can't see how these terms combine...

here goes:

$4[(.5)^4\cdot (.6)^3]+4[(.5)^4\cdot(.6)^3\cdot(.4)]=4[(.3)^3\cdot (.7)]$

I do understand where the $(.3)^3$ comes from, that is $.5\cdot.6 =.3$,

In simplifying the expression as follows, I arrive at $(2\cdot.3^3)+(2\cdot. 3^3\cdot .4)$

It is from here that I cannot figure out how this simplifies to $4[(.3)^3\cdot (.7)]$ Can anyone help with this?

PortMadeleineCrumpet
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    Divide by $4$, then note that $.5^4\times .6^3\times (1.4)=.5\times .3^3\times 1.4=.3^3\times .7$ as desired. – lulu May 07 '20 at 23:30
  • Thank you. I apologize but I’m having a little bit of trouble understanding. Which term do I divide by 4? Also, why is it ok for me to divide by 4? – PortMadeleineCrumpet May 07 '20 at 23:56
  • "why is it okay for me to divide by $4$" If you just divide by $4$ by itself... I agree you should be concerned. I think it is better phrased as factor out a $4$. Recall that $ab+ac=a(b+c)$, so here we have $4[***]+4[\cdots]$ which can simplify as $4(***+\cdots)$ where I didn't bother writing out what was inside the bracketed expressions. Now, all our attention can be solely on the bracketed expressions. – JMoravitz May 08 '20 at 00:13

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