Multiplication Properties of an Exponent

[jramirez23]

Recently, I ran into a strange problem of when I was doing my practice on Multiplying Polynomials. I do know the answer to the problem, I just have a question:

4w[sup:2cldy8x3]2[/sup:2cldy8x3](3w[sup:2cldy8x3]3[/sup:2cldy8x3] minus 2w[sup:2cldy8x3]2[/sup:2cldy8x3] minus w)

I realize that to find the product of this problem, I must distribute the 4w[sup:2cldy8x3]2[/sup:2cldy8x3] to every term in the equation. That is just what I did. I had no problems doing this to every term except 3w[sup:2cldy8x3]3[/sup:2cldy8x3]. This was because I couldn't tell if the outcome of this was to be a 12w[sup:2cldy8x3]5[/sup:2cldy8x3] or a 12w[sup:2cldy8x3]6[/sup:2cldy8x3]. Can anyone provide any clarification on this?

 

[stapel]

4w[sup:22oa125s]2[/sup:22oa125s](3w[sup:22oa125s]3[/sup:22oa125s] minus 2w[sup:22oa125s]2[/sup:22oa125s] minus w)

...every term except 3w[sup:22oa125s]3[/sup:22oa125s]....I couldn't tell if the outcome of this was to be a 12w[sup:22oa125s]5[/sup:22oa125s] or a 12w[sup:22oa125s]6[/sup:22oa125s].

When in doubt, return to the definition:

. . . . .w[sup:22oa125s]2[/sup:22oa125s] = ww

. . . . .w[sup:22oa125s]3[/sup:22oa125s] = www

. . . . .(w[sup:22oa125s]2[/sup:22oa125s])(w[sup:22oa125s]3[/sup:22oa125s]) = (ww)(www) = wwwww

How does that last expression simplify? :wink:

Eliz.

 

[sgtpepper]

You're mixing up:

x^2 * x^3 = x^5

and
(x^2)^3 = x^6

that's all. Try and plug in values for x, to see whether what I've just told you is actually true!


http://tinyurl.com/yploc4